Curso_de_Estatística_Parte_1.ipynb

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      "cell_type": "markdown",
      "metadata": {
        "id": "WvMflodMjQKe"
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      "source": [
        "***\n",
        "# <font color=green size=10>CURSO DE ESTATÍSTICA - PARTE 1</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cVgsZ_E3jQKg"
      },
      "source": [
        "# <font color=green>1 CONHECENDO OS DADOS</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TDjqYYNojQKh"
      },
      "source": [
        "## <font color=green>1.1 Dataset do projeto</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iN1gIbaKjQKh"
      },
      "source": [
        "### Pesquisa Nacional por Amostra de Domicílios - 2015\n",
        "\n",
        "A <b>Pesquisa Nacional por Amostra de Domicílios - PNAD</b> investiga anualmente, de forma permanente, características gerais da população, de educação, trabalho, rendimento e habitação e outras, com periodicidade variável, de acordo com as necessidades de informação para o país, como as características sobre migração, fecundidade, nupcialidade, saúde, segurança alimentar, entre outros temas. O levantamento dessas estatísticas constitui, ao longo dos 49 anos de realização da pesquisa, um importante instrumento para formulação, validação e avaliação de políticas orientadas para o desenvolvimento socioeconômico e a melhoria das condições de vida no Brasil."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U6V7br1RjQKi"
      },
      "source": [
        "### Fonte dos Dados\n",
        "\n",
        "https://ww2.ibge.gov.br/home/estatistica/populacao/trabalhoerendimento/pnad2015/microdados.shtm"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r0Fe_qnzjQKj"
      },
      "source": [
        "### Variáveis utilizadas\n",
        "\n",
        "> ### Renda\n",
        "> ***\n",
        "\n",
        "Rendimento mensal do trabalho principal para pessoas de 10 anos ou mais de idade.\n",
        "\n",
        "> ### Idade\n",
        "> ***\n",
        "\n",
        "Idade do morador na data de referência em anos.\n",
        "\n",
        "> ### Altura (elaboração própria)\n",
        "> ***\n",
        "\n",
        "Altura do morador em metros.\n",
        "\n",
        "> ### UF\n",
        "> ***\n",
        "\n",
        "|Código|Descrição|\n",
        "|---|---|\n",
        "|11|Rondônia|\n",
        "|12|Acre|\n",
        "|13|Amazonas|\n",
        "|14|Roraima|\n",
        "|15|Pará|\n",
        "|16|Amapá|\n",
        "|17|Tocantins|\n",
        "|21|Maranhão|\n",
        "|22|Piauí|\n",
        "|23|Ceará|\n",
        "|24|Rio Grande do Norte|\n",
        "|25|Paraíba|\n",
        "|26|Pernambuco|\n",
        "|27|Alagoas|\n",
        "|28|Sergipe|\n",
        "|29|Bahia|\n",
        "|31|Minas Gerais|\n",
        "|32|Espírito Santo|\n",
        "|33|Rio de Janeiro|\n",
        "|35|São Paulo|\n",
        "|41|Paraná|\n",
        "|42|Santa Catarina|\n",
        "|43|Rio Grande do Sul|\n",
        "|50|Mato Grosso do Sul|\n",
        "|51|Mato Grosso|\n",
        "|52|Goiás|\n",
        "|53|Distrito Federal|\n",
        "\n",
        "> ### Sexo\n",
        "> ***\n",
        "\n",
        "|Código|Descrição|\n",
        "|---|---|\n",
        "|0|Masculino|\n",
        "|1|Feminino|\n",
        "\n",
        "> ### Anos de Estudo\n",
        "> ***\n",
        "\n",
        "|Código|Descrição|\n",
        "|---|---|\n",
        "|1|Sem instrução e menos de 1 ano|\n",
        "|2|1 ano|\n",
        "|3|2 anos|\n",
        "|4|3 anos|\n",
        "|5|4 anos|\n",
        "|6|5 anos|\n",
        "|7|6 anos|\n",
        "|8|7 anos|\n",
        "|9|8 anos|\n",
        "|10|9 anos|\n",
        "|11|10 anos|\n",
        "|12|11 anos|\n",
        "|13|12 anos|\n",
        "|14|13 anos|\n",
        "|15|14 anos|\n",
        "|16|15 anos ou mais|\n",
        "|17|Não determinados|\n",
        "||Não aplicável|\n",
        "\n",
        "> ### Cor\n",
        "> ***\n",
        "\n",
        "|Código|Descrição|\n",
        "|---|---|\n",
        "|0|Indígena|\n",
        "|2|Branca|\n",
        "|4|Preta|\n",
        "|6|Amarela|\n",
        "|8|Parda|\n",
        "|9|Sem declaração|"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OK1IQH5cX7Gb"
      },
      "source": [
        "#### <font color='red'>Observação</font>\n",
        "***\n",
        "> Os seguintes tratamentos foram realizados nos dados originais:\n",
        "> 1. Foram eliminados os registros onde a <b>Renda</b> era inválida (999 999 999 999);\n",
        "> 2. Foram eliminados os registros onde a <b>Renda</b> era missing;\n",
        "> 3. Foram considerados somente os registros das <b>Pessoas de Referência</b> de cada domicílio (responsável pelo domicílio)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Rw70V6ojQKk"
      },
      "source": [
        "### Importando pandas e lendo o dataset do projeto\n",
        "\n",
        "https://pandas.pydata.org/"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "8QgOpE-wjQKl"
      },
      "outputs": [],
      "source": [
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "ufRZ7TLwjQKo"
      },
      "outputs": [],
      "source": [
        "dados = pd.read_csv('dados.csv')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
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          "base_uri": "https://localhost:8080/"
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        "outputId": "adf01128-f119-4af6-87a4-aad8aac345d3",
        "scrolled": true
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      "outputs": [
        {
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            "text/plain": [
              "pandas.core.frame.DataFrame"
            ]
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          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "type(dados)"
      ]
    },
    {
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      "source": [
        "dados"
      ],
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      "execution_count": 36,
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              "       UF  Sexo  Idade  Cor  Anos de Estudo  Renda    Altura\n",
              "0      11     0     23    8              12    800  1.603808\n",
              "1      11     1     23    2              12   1150  1.739790\n",
              "2      11     1     35    8              15    880  1.760444\n",
              "3      11     0     46    2               6   3500  1.783158\n",
              "4      11     1     47    8               9    150  1.690631\n",
              "...    ..   ...    ...  ...             ...    ...       ...\n",
              "76835  53     1     46    2              11    812  1.687030\n",
              "76836  53     0     30    4               7   1500  1.792934\n",
              "76837  53     0     32    8              12   1300  1.830587\n",
              "76838  53     0     57    8               4   1500  1.726344\n",
              "76839  53     0     38    8               4    900  1.658305\n",
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              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-2bb0e0be-cc7b-4606-a3df-9b19f16bfa61 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dados.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "g73-ilufplBG",
        "outputId": "1aca0ae2-e636-4d83-c547-df85a6e291bd"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   UF  Sexo  Idade  Cor  Anos de Estudo  Renda    Altura\n",
              "0  11     0     23    8              12    800  1.603808\n",
              "1  11     1     23    2              12   1150  1.739790\n",
              "2  11     1     35    8              15    880  1.760444\n",
              "3  11     0     46    2               6   3500  1.783158\n",
              "4  11     1     47    8               9    150  1.690631"
            ],
            "text/html": [
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              "      <th>UF</th>\n",
              "      <th>Sexo</th>\n",
              "      <th>Idade</th>\n",
              "      <th>Cor</th>\n",
              "      <th>Anos de Estudo</th>\n",
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              "      <th>Altura</th>\n",
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              "      <td>1.739790</td>\n",
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              "    <tr>\n",
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              "      <td>6</td>\n",
              "      <td>3500</td>\n",
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              "      <td>8</td>\n",
              "      <td>9</td>\n",
              "      <td>150</td>\n",
              "      <td>1.690631</td>\n",
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              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
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              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-07bf5740-8e7c-4a4a-a377-0fa71cd62d61 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-07bf5740-8e7c-4a4a-a377-0fa71cd62d61');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-30d0fbe8-3b0b-48ae-82f1-9b48f22c0bfd\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-30d0fbe8-3b0b-48ae-82f1-9b48f22c0bfd')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-30d0fbe8-3b0b-48ae-82f1-9b48f22c0bfd button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E3Mx0tVqjQKs"
      },
      "source": [
        "## <font color=green>1.2 Tipos de dados</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oB4TCBFojQKt"
      },
      "source": [
        "### Variáveis qualitativas ordinais\n",
        "\n",
        "► Variáveis que podem ser ordenadas ou hierarquizardas"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NtQZNGNbjQKt",
        "outputId": "a56a89e6-f2b8-4970-a11e-a48e9014df32"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ],
      "source": [
        "sorted(dados['Anos de Estudo'].unique())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i2mCIMyojQKv"
      },
      "source": [
        "### Variáveis qualitativas nominais\n",
        "\n",
        "► Variáveis que não podem ser ordenadas ou hierarquizardas"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NODtY5IxjQKw",
        "outputId": "6eb6316c-cde1-4cd5-cfc9-60778d034710",
        "scrolled": true
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[11,\n",
              " 12,\n",
              " 13,\n",
              " 14,\n",
              " 15,\n",
              " 16,\n",
              " 17,\n",
              " 21,\n",
              " 22,\n",
              " 23,\n",
              " 24,\n",
              " 25,\n",
              " 26,\n",
              " 27,\n",
              " 28,\n",
              " 29,\n",
              " 31,\n",
              " 32,\n",
              " 33,\n",
              " 35,\n",
              " 41,\n",
              " 42,\n",
              " 43,\n",
              " 50,\n",
              " 51,\n",
              " 52,\n",
              " 53]"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ],
      "source": [
        "sorted(dados['UF'].unique())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NURfft2QjQKy",
        "outputId": "aaed7bad-a0fd-4b17-8fd1-62b689740c64"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0, 1]"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ],
      "source": [
        "sorted(dados['Sexo'].unique())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6VwGyqxMjQK1",
        "outputId": "3b00cf40-0a1d-418c-ae21-1b4eb926e4dc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0, 2, 4, 6, 8]"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "sorted(dados['Cor'].unique())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FQhi81LsjQK5"
      },
      "source": [
        "### Variáveis quantitativas discretas\n",
        "\n",
        "► Variáveis que representam uma contagem onde os valores possíveis formam um conjunto finito ou enumerável."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sr4JXeZkjQK5",
        "outputId": "3e60bf72-031a-4d4a-bea5-6c3e73b1a965"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "De 13 até 99 anos\n"
          ]
        }
      ],
      "source": [
        "print('De %s até %s anos' % (dados.Idade.min(), dados.Idade.max()))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7mMXLTukjQK-"
      },
      "source": [
        "#### <font color='red'>Observação</font>\n",
        "***\n",
        "> A variável idade pode ser classificada de três formas distintas:\n",
        "> 1. <b>QUANTITATIVA DISCRETA</b> - quando representa anos completos (números inteiros);\n",
        "> 2. <b>QUANTITATIVA CONTÍNUA</b> - quando representa a idade exata, sendo representado por frações de anos; e\n",
        "> 3. <b>QUALITATIVA ORDINAL</b> - quando representa faixas de idade."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J0L2OkaQjQK7"
      },
      "source": [
        "### Variáveis quantitativas contínuas\n",
        "\n",
        "► Variáveis que representam uma contagem ou mensuração que assumem valores em uma escala contínua (números reais)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jOW-bGyRjQK8",
        "outputId": "05359d28-2e9e-455f-8f12-6a6935ef0da6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "De 1.339244614 até 2.028496765 anos\n"
          ]
        }
      ],
      "source": [
        "print('De %s até %s anos' % (dados['Altura'].min(), dados.Altura.max()))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d_LW5gMIjQK_"
      },
      "source": [
        "### Classificação de uma variável\n",
        "<img src='https://caelum-online-public.s3.amazonaws.com/1177-estatistica-parte1/01/img001.png' width='70%'>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PNIg_4VEjQK_"
      },
      "source": [
        "# <font color=green>2 DISTRIBUIÇÃO DE FREQUÊNCIAS</font>\n",
        "***\n",
        "\n",
        "O primeiro passo em um trabalho de análise é o conhecimento do comportamento das variáveis envolvidas no estudo. Utilizando técnicas estatísticas como as análises das <b>DISTRIBUIÇÕES DE FREQUÊNCIAS</b> e <b>HISTOGRAMAS</b> podemos avaliar melhor a forma como os fenômenos em estudo se distribuem."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JhpyjkEFjQLA"
      },
      "source": [
        "## <font color=green>2.1 Distribuição de frequências para variáveis qualitativas</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SsN3ikjqjQLB"
      },
      "source": [
        "### Método 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dj_v0M44X7G3"
      },
      "source": [
        "https://pandas.pydata.org/pandas-docs/version/0.22/generated/pandas.Series.value_counts.html"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "id": "cA4gUboZjQLB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cd0311d1-57ca-4557-b901-23f47baa27a3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    53250\n",
              "1    23590\n",
              "Name: Sexo, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ],
      "source": [
        "dados['Sexo'].value_counts()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "iy4-ijknjQLD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "73fe03c2-f5c3-4add-a772-54aac8707bda"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    69.299844\n",
              "1    30.700156\n",
              "Name: Sexo, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ],
      "source": [
        "dados['Sexo'].value_counts(normalize = True) * 100"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "qfkiLcFijQLG"
      },
      "outputs": [],
      "source": [
        "frequencia = dados['Sexo'].value_counts()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "t4uFMt6fjQLI"
      },
      "outputs": [],
      "source": [
        "percentual = dados['Sexo'].value_counts(normalize = True) * 100"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "zUGfju86jQLM"
      },
      "outputs": [],
      "source": [
        "dist_freq_qualitativas = pd.DataFrame({'Frequência': frequencia, 'Porcentagem (%)': percentual})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "id": "kPOYfijijQLO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "outputId": "39ca259e-30d9-4167-d877-52cbd3bd8808"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Frequência  Porcentagem (%)\n",
              "0       53250        69.299844\n",
              "1       23590        30.700156"
            ],
            "text/html": [
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              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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              "\n",
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              "      --bg-color: #3B4455;\n",
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              "\n",
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              "    fill: var(--button-hover-fill-color);\n",
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              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "\n",
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              "      border-right-color: var(--fill-color);\n",
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              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
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              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
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              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
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              "    })();\n",
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              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ],
      "source": [
        "dist_freq_qualitativas"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "tMS-VSk3jQLQ"
      },
      "outputs": [],
      "source": [
        "dist_freq_qualitativas.rename(index = {0: 'Masculino', 1: 'Feminino'}, inplace = True)\n",
        "dist_freq_qualitativas.rename_axis('Sexo', axis = 'columns',inplace = True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "id": "B9zkYdcCyHe6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "outputId": "807e1c6c-14aa-4394-d68a-f44c8616a5a8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Sexo       Frequência  Porcentagem (%)\n",
              "Masculino       53250        69.299844\n",
              "Feminino        23590        30.700156"
            ],
            "text/html": [
              "\n",
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              "      <th>Sexo</th>\n",
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              "      <th>Porcentagem (%)</th>\n",
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              "      buttonEl.style.display =\n",
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              "        const element = document.querySelector('#df-2f941bca-6bd0-4fac-8714-2a7bd64c4127');\n",
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              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
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              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
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              "        const charts = await google.colab.kernel.invokeFunction(\n",
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              "        console.error('Error during call to suggestCharts:', error);\n",
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              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
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            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ],
      "source": [
        "dist_freq_qualitativas"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dados = pd.DataFrame({'Profissão': [1, 2, 3, 1, 2, 2, 2, 3, 3, 2, 1, 3]})\n",
        "frequencia = dados['Profissão'].value_counts()\n",
        "percentual = dados['Profissão'].value_counts(normalize = True) * 100\n",
        "dist_freq_qualitativas = pd.DataFrame({'Frequência': frequencia, 'Porcentagem (%)': percentual})\n",
        "dist_freq_qualitativas.rename(index = {1: 'Estatístico', 2: 'Cientista de Dados', 3: 'Programador Python'}, inplace = True)\n",
        "dist_freq_qualitativas.rename_axis('Profissão', axis= 'columns', inplace = True)\n",
        "dist_freq_qualitativas"
      ],
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          "base_uri": "https://localhost:8080/",
          "height": 143
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        "outputId": "74c71c10-282b-4390-d531-7a20f84019e0"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Profissão           Frequência  Porcentagem (%)\n",
              "Cientista de Dados           5        41.666667\n",
              "Programador Python           4        33.333333\n",
              "Estatístico                  3        25.000000"
            ],
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              "  @keyframes spin {\n",
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          },
          "metadata": {},
          "execution_count": 52
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D82ocp_djQLR"
      },
      "source": [
        "### Método 2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rLbfeA_UX7HF"
      },
      "source": [
        "https://pandas.pydata.org/pandas-docs/version/0.22/generated/pandas.crosstab.html"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dados = pd.read_csv('dados.csv')"
      ],
      "metadata": {
        "id": "VO1b1A5vj-on"
      },
      "execution_count": 63,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "id": "d8XMZiEfjQLS"
      },
      "outputs": [],
      "source": [
        "sexo = {0: 'Masculino',\n",
        "        1: 'Feminino'}\n",
        "\n",
        "cor = {0: 'Indígena',\n",
        "       2: 'Branca',\n",
        "       4: 'Preta',\n",
        "       6: 'Amarela',\n",
        "       8: 'Parda',\n",
        "       9: 'Sem declaração'}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
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          "height": 143
        },
        "outputId": "d273ab83-bc17-41c1-f872-57a2c92c0970"
      },
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        {
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            "text/plain": [
              "Cor        Indígena  Branca  Preta  Amarela  Parda\n",
              "Sexo                                              \n",
              "Masculino       256   22194   5502      235  25063\n",
              "Feminino        101    9621   2889      117  10862"
            ],
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              "        document.querySelector('#df-cc6fa368-b5ed-4807-9b38-a37749b97157 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-cc6fa368-b5ed-4807-9b38-a37749b97157');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-4acdd2ba-ca04-489b-b5ee-e3c4179b6303\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-4acdd2ba-ca04-489b-b5ee-e3c4179b6303')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
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              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
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              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
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              "    border-radius: 50%;\n",
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              "    width: 32px;\n",
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              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
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              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-4acdd2ba-ca04-489b-b5ee-e3c4179b6303 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ],
      "source": [
        "frequencia = pd.crosstab(dados.Sexo,dados.Cor)\n",
        "frequencia.rename(index = sexo, inplace = True)\n",
        "frequencia.rename(columns = cor, inplace = True)\n",
        "frequencia"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "id": "nrDtcf5gjQLV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "outputId": "bbca59e3-f112-4305-b21f-9bd5ffad1e49"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Cor        Indígena     Branca     Preta   Amarela      Parda\n",
              "Sexo                                                         \n",
              "Masculino  0.333160  28.883394  7.160333  0.305830  32.617126\n",
              "Feminino   0.131442  12.520822  3.759761  0.152264  14.135867"
            ],
            "text/html": [
              "\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>Cor</th>\n",
              "      <th>Indígena</th>\n",
              "      <th>Branca</th>\n",
              "      <th>Preta</th>\n",
              "      <th>Amarela</th>\n",
              "      <th>Parda</th>\n",
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              "      <th>Sexo</th>\n",
              "      <th></th>\n",
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              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Masculino</th>\n",
              "      <td>0.333160</td>\n",
              "      <td>28.883394</td>\n",
              "      <td>7.160333</td>\n",
              "      <td>0.305830</td>\n",
              "      <td>32.617126</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Feminino</th>\n",
              "      <td>0.131442</td>\n",
              "      <td>12.520822</td>\n",
              "      <td>3.759761</td>\n",
              "      <td>0.152264</td>\n",
              "      <td>14.135867</td>\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-1cf4f037-c892-4800-a524-69afff937849 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-1cf4f037-c892-4800-a524-69afff937849');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
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              "\n",
              "\n",
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              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
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              "    display: none;\n",
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              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-cd644708-1f56-4427-9764-57a27384fcb1 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ],
      "source": [
        "frequencia = pd.crosstab(dados.Sexo,dados.Cor,normalize = True) * 100\n",
        "frequencia.rename(index = sexo, inplace = True)\n",
        "frequencia.rename(columns = cor, inplace = True)\n",
        "frequencia"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "id": "_MHwBGcdp6dl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "outputId": "94b840fe-7e97-4c63-8984-deb43b869092"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Cor           Indígena       Branca        Preta      Amarela        Parda\n",
              "Sexo                                                                      \n",
              "Masculino  1081.710938  2925.744435  1603.861687  4758.251064  1659.577425\n",
              "Feminino   2464.386139  2109.866750  1134.596400  3027.341880  1176.758516"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-cf730d31-7d0d-4ab4-8956-e542a0b75afc\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
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              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>Cor</th>\n",
              "      <th>Indígena</th>\n",
              "      <th>Branca</th>\n",
              "      <th>Preta</th>\n",
              "      <th>Amarela</th>\n",
              "      <th>Parda</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Sexo</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Masculino</th>\n",
              "      <td>1081.710938</td>\n",
              "      <td>2925.744435</td>\n",
              "      <td>1603.861687</td>\n",
              "      <td>4758.251064</td>\n",
              "      <td>1659.577425</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Feminino</th>\n",
              "      <td>2464.386139</td>\n",
              "      <td>2109.866750</td>\n",
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              "      <td>3027.341880</td>\n",
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              "        const element = document.querySelector('#df-cf730d31-7d0d-4ab4-8956-e542a0b75afc');\n",
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              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
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              "\n",
              "  @keyframes spin {\n",
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              "\n",
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              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
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              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ],
      "source": [
        "frequencia = pd.crosstab(dados.Sexo,dados.Cor,aggfunc = 'mean',values = dados.Renda)\n",
        "frequencia.rename(index = sexo, inplace = True)\n",
        "frequencia.rename(columns = cor, inplace = True)\n",
        "frequencia"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eaXQUxnXjQLa"
      },
      "source": [
        "## <font color=green>2.2 Distribuição de frequências para variáveis quantitativas (classes personalizadas)</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wxsSD-VVjQLb"
      },
      "source": [
        "### Passo 1 - Especificar os limites de cada classe\n",
        "\n",
        "Utilizar a seguinte classificação:\n",
        "\n",
        "<b>A</b> ► Acima de 20 SM\n",
        "\n",
        "<b>B</b> ► De 10 a 20 SM\n",
        "\n",
        "<b>C</b> ► De 4 a 10 SM\n",
        "\n",
        "<b>D</b> ► De 2 a 4 SM\n",
        "\n",
        "<b>E</b> ► Até 2 SM\n",
        "\n",
        "onde <b>SM</b> é o valor do salário mínimo na época. Em nosso caso <b>R$ 788,00</b> (2015):\n",
        "\n",
        "<b>A</b> ► Acima de 15.760\n",
        "\n",
        "<b>B</b> ► De 7.880 a 15.760\n",
        "\n",
        "<b>C</b> ► De 3.152 a 7.880\n",
        "\n",
        "<b>D</b> ► De 1.576 a 3.152\n",
        "\n",
        "<b>E</b> ► Até 1.576\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "id": "Z08790GUjQLc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ae1547fd-7c7e-4bc7-92d2-c51b01642aa1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ],
      "source": [
        "dados.Renda.min()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "id": "5q2V5-0FjQLe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e1f83bd6-a661-4ea9-a255-be4de9c8273d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "200000"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ],
      "source": [
        "dados.Renda.max()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {
        "id": "Qt5F5w2UjQLg"
      },
      "outputs": [],
      "source": [
        "classes = [0, 1576, 3152, 7880, 15760, 200000]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "id": "DKPIGOLLjQLi"
      },
      "outputs": [],
      "source": [
        "labels = ['E', 'D', 'C', 'B', 'A']"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IQhlvrQUjQLk"
      },
      "source": [
        "### Passo 2 - Criar a tabela de frequências"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Uy3fH4IxX7Hc"
      },
      "source": [
        "https://pandas.pydata.org/pandas-docs/version/0.22/generated/pandas.cut.html"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "N-wZ_2UajQLm"
      },
      "outputs": [],
      "source": [
        "pd.cut(x = dados.Renda,\n",
        "       bins = classes,\n",
        "       labels = labels,\n",
        "       include_lowest = True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "id": "WrZ2m2GajQLo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0a5ea076-65c3-48bb-ac0f-3aba346d5c86"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "E    49755\n",
              "D    16700\n",
              "C     7599\n",
              "B     2178\n",
              "A      608\n",
              "Name: Renda, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 76
        }
      ],
      "source": [
        "frequencia = pd.value_counts(\n",
        "  pd.cut(x = dados.Renda,\n",
        "       bins = classes,\n",
        "       labels = labels,\n",
        "       include_lowest = True)\n",
        ")\n",
        "frequencia"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "id": "btKoxJDujQLp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "345dc6ff-035e-4b15-d9a6-b4f9e61f2ac0"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "E    0.647514\n",
              "D    0.217335\n",
              "C    0.098894\n",
              "B    0.028345\n",
              "A    0.007913\n",
              "Name: Renda, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ],
      "source": [
        "percentual = pd.value_counts(\n",
        "  pd.cut(x = dados.Renda,\n",
        "       bins = classes,\n",
        "       labels = labels,\n",
        "       include_lowest = True),\n",
        "  normalize = True\n",
        ")\n",
        "percentual"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "id": "uTMEJXUHjQLs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "4fb6e814-6cd8-4d5c-faf9-9e53c4928ba1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Frequência  Porcentagem (%)\n",
              "E       49755         0.647514\n",
              "D       16700         0.217335\n",
              "C        7599         0.098894\n",
              "B        2178         0.028345\n",
              "A         608         0.007913"
            ],
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              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 82
        }
      ],
      "source": [
        "dist_freq_quantitativas_personalizadas = pd.DataFrame({'Frequência' : frequencia, 'Porcentagem (%)' : percentual})\n",
        "dist_freq_quantitativas_personalizadas"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dist_freq_quantitativas_personalizadas.sort_index(ascending = True)"
      ],
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        "id": "OT8-GPb8pvpz",
        "outputId": "fd467ac5-a92c-4d77-dcd1-7b1b4e0e76f0"
      },
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Frequência  Porcentagem (%)\n",
              "E       49755         0.647514\n",
              "D       16700         0.217335\n",
              "C        7599         0.098894\n",
              "B        2178         0.028345\n",
              "A         608         0.007913"
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          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "classes = [dados.Altura.min(), 1.65, 1.75, dados.Altura.max()]\n",
        "labels = ['1 - Baixa', '2 - Média', '3 - Alta']\n",
        "\n",
        "frequencia = pd.value_counts(\n",
        "    pd.cut(\n",
        "        x = dados.Altura,\n",
        "        bins = classes,\n",
        "        labels = labels,\n",
        "        include_lowest = True\n",
        "    )\n",
        ")\n",
        "\n",
        "percentual = pd.value_counts(\n",
        "    pd.cut(\n",
        "        x = dados.Altura,\n",
        "        bins = classes,\n",
        "        labels = labels,\n",
        "        include_lowest = True\n",
        "    ), normalize = True\n",
        ") * 100\n",
        "\n",
        "dist_freq_altura = pd.DataFrame(\n",
        "    {'Frequência': frequencia, 'Porcentagem (%)': percentual}\n",
        ")\n",
        "\n",
        "dist_freq_altura.rename_axis('Estaturas', axis= 'columns', inplace = True)\n",
        "\n",
        "dist_freq_altura.sort_index(ascending = True, inplace = True)\n",
        "\n",
        "dist_freq_altura"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "-K2HZO8rq4W2",
        "outputId": "5cde9659-309b-4d44-cd3f-d73aca709a7d"
      },
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Estaturas  Frequência  Porcentagem (%)\n",
              "1 - Baixa       20529        26.716554\n",
              "2 - Média       36162        47.061426\n",
              "3 - Alta        20149        26.222020"
            ],
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              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-2f007c95-3d3e-4ba2-a5b4-a6bc3608cd96 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-2f007c95-3d3e-4ba2-a5b4-a6bc3608cd96');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-9dccf959-4c5d-4c0d-96f3-aa4a28285ed4\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-9dccf959-4c5d-4c0d-96f3-aa4a28285ed4')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-9dccf959-4c5d-4c0d-96f3-aa4a28285ed4 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Jth9r0JBq7m4"
      },
      "execution_count": 85,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ViJYvvjujQLu"
      },
      "source": [
        "## <font color=green>2.3 Distribuição de frequências para variáveis quantitativas (classes de amplitude fixa)</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "02ve2BVojQLv"
      },
      "source": [
        "### Importando bibliotecas\n",
        "\n",
        "http://www.numpy.org/"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hSIsHKuJjQLw"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s9UGNaMzjQLy"
      },
      "source": [
        "### Passo 1 - Difinindo o número de classes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p268tvNHjQLy"
      },
      "source": [
        "#### Regra de Sturges\n",
        "\n",
        "# $$k = 1 + \\frac {10}{3}\\log_{10}n$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wgLH6gGqjQLz"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uTuVep-8jQL0"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "988IDFNOjQL2"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "B_Y66_KFjQL4"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5eO-RhaljQL6"
      },
      "source": [
        "### Passo 2 - Criar a tabela de frequências"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sVVA-jvDjQL7"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-ylxSip1jQL9"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "n9kkJ0WTjQL_"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Js9iLwNkjQME"
      },
      "source": [
        "## <font color=green>2.4 Histograma</font>\n",
        "***\n",
        "\n",
        "O <b>HISTOGRAMA</b> é a representação gráfica de uma distribuição de frequências. É uma gráfico formado por um conjunto de retângulos colocados lado a lado, onde a área de cada retângulo é proporcional à frequência da classe que ele representa."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VzZEXDKX3PUH"
      },
      "source": [
        "### Importando a biblioteca\n",
        "\n",
        "https://seaborn.pydata.org/"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PYRaBCnxjQME"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GAX3aCa6jQMG"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wiQPnuMojQMJ"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3fySBW7qjQMK"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0HcLhLYtjQMM"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IQYnbxoS-kjQ"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uIb17Es3jQMP"
      },
      "source": [
        "# <font color=green>3 MEDIDAS DE TENDÊNCIA CENTRAL</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wrya4suEX7H-"
      },
      "source": [
        "## DataFrame de exemplo"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jj7a21flX7H_"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kcHJFW-YjQMP"
      },
      "source": [
        "## <font color=green>3.1 Média aritmética</font>\n",
        "***\n",
        "\n",
        "É representada por $\\mu$ quando se refere à população e por $\\bar{X}$ quando se refere à amostra\n",
        "\n",
        "# $$\\mu = \\frac 1n\\sum_{i=1}^{n}X_i$$\n",
        "\n",
        "onde\n",
        "\n",
        "$n$ = número de observações (registros)\n",
        "\n",
        "$X_i$ = valor da i-ésima observação (registro)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QW4JPcBmX7IA"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LuT8WNy5X7IB"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BRMZcmMEjQMQ"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CGgJbsK0HBQc"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9geu3UcKjQMS"
      },
      "source": [
        "## <font color=green>3.2 Mediana</font>\n",
        "***\n",
        "\n",
        "Para obtermos a mediana de uma conjunto de dados devemos proceder da seguinte maneira:\n",
        "1. Ordenar o conjunto de dados;\n",
        "2. Identificar o número de observações (registros) do conjunto de dados ($n$);\n",
        "3. Identicar o elemento mediano:\n",
        "\n",
        "> Quando $n$ for ímpar, a posição do elemento mediano será obtida da seguinte forma:\n",
        "\n",
        "\n",
        "# $$Elemento_{Md} = \\frac{n+1}2$$\n",
        "\n",
        "> Quando $n$ for par, a posição do elemento mediano será obtida da seguinte forma:\n",
        "\n",
        "\n",
        "# $$Elemento_{Md} = \\frac{n}2$$\n",
        "\n",
        "4. Obter a mediana:\n",
        "\n",
        "> Quando $n$ for ímpar:\n",
        "\n",
        "\n",
        "# $$Md = X_{Elemento_{Md}}$$\n",
        "\n",
        "> Quando $n$ for par:\n",
        "\n",
        "\n",
        "# $$Md = \\frac{X_{Elemento_{Md}} + X_{Elemento_{Md}+1}}2$$\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e0IuYdJFjQMT"
      },
      "source": [
        "### Exemplo 1 - n ímpar\n",
        "\n",
        "<img src='https://caelum-online-public.s3.amazonaws.com/1177-estatistica-parte1/01/img002.png' width='40%' style=\"float:left\">"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3dXjdRFlX7IH"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cU91DJ-yjQMV"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "z9bOnYKf1NOd"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "u3nfPEFjjQMW"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "trC12MHxjQMY"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NKccffcLjQMZ"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ody5mfXLjQMb"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hQHyjfLkjQMe"
      },
      "source": [
        "### Exemplo 2 - n par\n",
        "\n",
        "<img src='https://caelum-online-public.s3.amazonaws.com/1177-estatistica-parte1/01/img003.png' width='50%' style=\"float:left\">"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Jkx1WZenjQMe"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "D1LUpvZkYsHq"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PuiScCf0-vh9"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6wB1UztBjQMf"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tEBVXl7CjQMh"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "N-jSUjZSjQMi"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IevBBtrRjQMj"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nK27TxrkjQMl"
      },
      "source": [
        "### Obtendo a mediana em nosso dataset"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dJznpnjUjQMl"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "W4a5PVYdjQMm"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CmCu6BXQjQMo"
      },
      "source": [
        "## <font color=green>3.3 Moda</font>\n",
        "***\n",
        "\n",
        "Pode-se definir a moda como sendo o valor mais frequente de um conjunto de dados. A moda é bastante utilizada para dados qualitativos."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BHibMzw8X7Id"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xICDpQguX7Ik"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "x9lIRFESX7Il"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yUP6QFuiX7Io"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YwhBwz-JjQMr"
      },
      "source": [
        "### Obtendo a moda em nosso dataset"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mC8vvYk-jQMr"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Sdosy_vSX7Iw"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_-0gjQWFjQMu"
      },
      "source": [
        "## <font color=green>3.4 Relação entre média, mediana e moda</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0S7pa_jLjQMu"
      },
      "source": [
        "<img src='https://caelum-online-public.s3.amazonaws.com/1177-estatistica-parte1/01/img004.png' width='80%'>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b7ZchyFsjQMu"
      },
      "source": [
        "### Avaliando a variável RENDA"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "d8WQQ0PdjQMv"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "krws6f_SjQMw"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_Y7KpB25jQMx"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gQ0e56VajQMy"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nX6lnCBujQM0"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FnLQAxSijQM1"
      },
      "source": [
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WazchssNjQM1"
      },
      "source": [
        "### Avaliando a variável ALTURA"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "41uJsCk9jQM2"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EkgerGuXjQM3"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Jj6MFUXbjQM4"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "84X-3AzvjQM5"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PJIMB8i8jQM6"
      },
      "source": [
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eS4I2H7jjQM7"
      },
      "source": [
        "### Avaliando a variável ANOS DE ESTUDO"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NPCcjXqPjQM8"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PjfvPYUajQM9"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VF_Bj8x2jQM-"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ohqUZ5RsjQNA"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AwM8UvApjQNC"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vcaIo45UjQND"
      },
      "source": [
        "# <font color=green>4 MEDIDAS SEPARATRIZES</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f4XrApNxjQNE"
      },
      "source": [
        "## <font color=green>4.1 Quartis, decis e percentis</font>\n",
        "***\n",
        "\n",
        "Há uma série de medidas de posição semelhantes na sua concepção à mediana, embora não sejam medidas de tendência central. Como se sabe, a mediana divide a distribuição em duas partes iguais quanto ao número de elementos de cada parte. Já os quartis permitem dividir a distribuição em quatro partes iguais quanto ao número de elementos de cada uma; os decis em dez partes e os centis em cem partes iguais."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VmbdUO-ujQNE"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gyiJDAMbjQNF"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EpRKboV5jQNG"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LQW--GapjQNI",
        "scrolled": true
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pO2HCo1WUE5F"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GGHVrQA7jQNI"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6gIeZO_CjQNJ"
      },
      "source": [
        "## <font color=green>4.2 Box-plot</font>\n",
        "***\n",
        "\n",
        "O box plot dá uma idéia da posição, dispersão, assimetria, caudas e dados discrepantes (outliers). A posição central é dada pela mediana e a dispersão por $IIQ$. As posições relativas de $Q1$, $Mediana$ e $Q3$ dão uma noção da simetria da distribuição. Os comprimentos das cauda são dados pelas linhas que vão do retângulo aos valores remotos e pelos valores atípicos."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VeiTE_gvjQNK"
      },
      "source": [
        "<img src='https://caelum-online-public.s3.amazonaws.com/1177-estatistica-parte1/01/img005.png' width='65%'>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pBY2EWkzjQNK"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AEhX7-ggsuiY"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2ZPrRov1suSF"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CSwlKUrrsuFi"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IDrzBcJ_jQNL"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "V3I-2KsbjQNM"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "amloMZwVjQNN"
      },
      "source": [
        "<img src='https://caelum-online-public.s3.amazonaws.com/1177-estatistica-parte1/01/img006.png' width='80%'>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aJ6v_NI9jQNN"
      },
      "source": [
        "# <font color=green>5 MEDIDAS DE DISPERSÃO</font>\n",
        "***\n",
        "\n",
        "Embora as medidas de posição forneçam uma sumarização bastante importante dos dados, elas podem não ser suficientes para caracterizar conjuntos distintos, especialmente quando as observações de determinada distribuição apresentarem dados muito dispersos."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D6xVxAQ7jQNO"
      },
      "source": [
        "## <font color=green>5.1 Desvio médio absoluto</font>\n",
        "***\n",
        "\n",
        "\n",
        "# $$DM = \\frac 1n\\sum_{i=1}^{n}|X_i-\\bar{X}|$$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0sL31blV7nz3"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f3pAri4G7nc4"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8_Q2tOTmjQNO"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RWo0AhBEjQNP"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OiWDTw0ljQNQ"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qQbjktz5jQNR"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dtIDTt6djQNV"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "m4buiQWF01xt"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1PEJ_LUn01eV"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jSKfnKwEjQNW"
      },
      "source": [
        "## <font color=green>5.2 Variância</font>\n",
        "***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tHD3yNqzjQNW"
      },
      "source": [
        "### Variância\n",
        "\n",
        "A variância é construída a partir das diferenças entre cada observação e a média dos dados, ou seja, o desvio em torno da média. No cálculo da variância, os desvios em torno da média são elevados ao quadrado."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WrCn9hw0jQNX"
      },
      "source": [
        "### Variância populacional\n",
        "\n",
        "# $$\\sigma^2 = \\frac 1n\\sum_{i=1}^{n}(X_i-\\mu)^2$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jV5mQT_djQNX"
      },
      "source": [
        "### Variância amostral\n",
        "\n",
        "# $$S^2 = \\frac 1{n-1}\\sum_{i=1}^{n}(X_i-\\bar{X})^2$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4tlbCQeujQNZ"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oCcAfoIOjQNa"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EyrfPHLtjQNb"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wQl_CsytjQNg"
      },
      "source": [
        "## <font color=green>5.3 Desvio padrão</font>\n",
        "***\n",
        "\n",
        "Uma das restrições da variância é o fato de fornecer medidas em quadrados das unidades originais - a variância de medidas de comprimento, por exemplo, é em unidades de área. Logo, o fato de as unidades serem diferentes dificulta a comparação da dispersão com as variáveis que a definem. Um modo de eliminar essa dificuldade é considerar sua raiz quadrada."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X9w1Iqt3jQNg"
      },
      "source": [
        "### Desvio padrão populacional\n",
        "\n",
        "# $$\\sigma = \\sqrt{\\frac 1n\\sum_{i=1}^{n}(X_i-\\mu)^2} \\Longrightarrow \\sigma = \\sqrt{\\sigma^2}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D3J4MvMpjQNg"
      },
      "source": [
        "### Desvio padrão amostral\n",
        "\n",
        "# $$S = \\sqrt{\\frac 1{n-1}\\sum_{i=1}^{n}(X_i-\\bar{X})^2} \\Longrightarrow S = \\sqrt{S^2}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2di6iLFaSPda"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BMTx9yKHSPON"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_PeQtqbdjQNh"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5LYOKy25jQNi"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FfcyfSkFjQNj"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "G8vorygCjQNk"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "01op3BEvjQNl"
      },
      "outputs": [],
      "source": []
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aiUvZluhUx-0"
      },
      "outputs": [],
      "source": []
    }
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