Data_handling.ipynb

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      "source": [
        "#importing Important Libraries\n",
        "import pandas as pd\n",
        "import numpy as np"
      ]
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      "cell_type": "code",
      "source": [
        "df = pd.read_csv('/content/class-grades.csv', header=None, sep = '\\n')\n",
        "df = df[0].str.split(',', expand=True)\n",
        "\n",
        "\n",
        "# header=0--> deletes column names(header) and assign new column names(if we pass)\n",
        "#expand = True --> the split elements will expand out into separate columns"
      ],
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        "# Dataset Description\n",
        "Grades from a Chemical Engineering course at McMaster University.\n",
        "Data source:\t\n",
        "The recorded values are the average of sub-components: e.g the Tutorial variable is the average of all tutorials, the Final exam variable is the average of all questions in the final, written exam.\n",
        "\n",
        "The Prefix column is the year in which the student first enrolls at the university and is a crude approximation of the student's age (maturity).\n",
        "\n",
        "This particular course permitted students to work in groups for assignments, tutorials and the take-home exam. The groups were self-selected, and varied during the semester.\n",
        "\n",
        "Of interest is whether the assignments, tutorials, midterms or take-home exam are a good predictor of the student's performance in the final exam. Also, does the Prefix variable show any promise as a prediction variable?"
      ],
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        "df.head()"
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              "        0           1         2        3         4      5     6\n",
              "0  Prefix  Assignment  Tutorial  Midterm  TakeHome  Final  None\n",
              "1      05       57.14     34.09    64.38     51.48  52.50  None\n",
              "2      08       95.05    105.49    67.50     99.07  68.33  None\n",
              "3      08       83.70     83.17     30.0     63.15  48.89  None\n",
              "4      07       81.22     96.06    49.38    105.93  80.56  None"
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      "source": [
        "#header_row = 0\n",
        "#df.columns = df.iloc[header_row]\n",
        "#print(df)"
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      "source": [
        "Since Header (Column Names) are in first row of dataset, we need to Move that as Header"
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        "df.columns = df.iloc[0]\n",
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              "0  Prefix  Assignment  Tutorial  Midterm  TakeHome  Final   NaN\n",
              "0  Prefix  Assignment  Tutorial  Midterm  TakeHome  Final  None\n",
              "1      05       57.14     34.09    64.38     51.48  52.50  None\n",
              "2      08       95.05    105.49    67.50     99.07  68.33  None\n",
              "3      08       83.70     83.17     30.0     63.15  48.89  None\n",
              "4      07       81.22     96.06    49.38    105.93  80.56  None"
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              "Index(['Prefix', 'Assignment', 'Tutorial', 'Midterm', 'TakeHome', 'Final',\n",
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        "#header_row = df.iloc[0]\n",
        "#df.columns = header_row"
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        "header_row = df.iloc[0]\n",
        "df = pd.DataFrame(df.values[1:], columns=header_row)\n",
        "df.head()"
      ],
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              "      <th>0</th>\n",
              "      <td>05</td>\n",
              "      <td>57.14</td>\n",
              "      <td>34.09</td>\n",
              "      <td>64.38</td>\n",
              "      <td>51.48</td>\n",
              "      <td>52.50</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>08</td>\n",
              "      <td>95.05</td>\n",
              "      <td>105.49</td>\n",
              "      <td>67.50</td>\n",
              "      <td>99.07</td>\n",
              "      <td>68.33</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>08</td>\n",
              "      <td>83.70</td>\n",
              "      <td>83.17</td>\n",
              "      <td>30.0</td>\n",
              "      <td>63.15</td>\n",
              "      <td>48.89</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>07</td>\n",
              "      <td>81.22</td>\n",
              "      <td>96.06</td>\n",
              "      <td>49.38</td>\n",
              "      <td>105.93</td>\n",
              "      <td>80.56</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>08</td>\n",
              "      <td>91.32</td>\n",
              "      <td>93.64</td>\n",
              "      <td>95.0</td>\n",
              "      <td>107.41</td>\n",
              "      <td>73.89</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-8a844ef0-1f65-4c26-bd5c-c46c895af806')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\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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              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
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              "\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",
              "    [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-8a844ef0-1f65-4c26-bd5c-c46c895af806 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-8a844ef0-1f65-4c26-bd5c-c46c895af806');\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",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "0 Prefix Assignment Tutorial Midterm TakeHome  Final   NaN\n",
              "0     05      57.14    34.09   64.38    51.48  52.50  None\n",
              "1     08      95.05   105.49   67.50    99.07  68.33  None\n",
              "2     08      83.70    83.17    30.0    63.15  48.89  None\n",
              "3     07      81.22    96.06   49.38   105.93  80.56  None\n",
              "4     08      91.32    93.64    95.0   107.41  73.89  None"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df=df[df.columns.dropna()] #dropping Null Values"
      ],
      "metadata": {
        "id": "8NTB_OdULPFp"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "1x3YvS9mLPA6",
        "outputId": "8950f35d-c9d2-4a9a-ad9f-d65d88139edc"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-71e9a8a0-67f7-498d-9891-5ded69d510f1\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        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></th>\n",
              "      <th>Prefix</th>\n",
              "      <th>Assignment</th>\n",
              "      <th>Tutorial</th>\n",
              "      <th>Midterm</th>\n",
              "      <th>TakeHome</th>\n",
              "      <th>Final</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
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              "      <th>0</th>\n",
              "      <td>05</td>\n",
              "      <td>57.14</td>\n",
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              "      <td>51.48</td>\n",
              "      <td>52.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>08</td>\n",
              "      <td>95.05</td>\n",
              "      <td>105.49</td>\n",
              "      <td>67.50</td>\n",
              "      <td>99.07</td>\n",
              "      <td>68.33</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>08</td>\n",
              "      <td>83.70</td>\n",
              "      <td>83.17</td>\n",
              "      <td>30.0</td>\n",
              "      <td>63.15</td>\n",
              "      <td>48.89</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>07</td>\n",
              "      <td>81.22</td>\n",
              "      <td>96.06</td>\n",
              "      <td>49.38</td>\n",
              "      <td>105.93</td>\n",
              "      <td>80.56</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>08</td>\n",
              "      <td>91.32</td>\n",
              "      <td>93.64</td>\n",
              "      <td>95.0</td>\n",
              "      <td>107.41</td>\n",
              "      <td>73.89</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-71e9a8a0-67f7-498d-9891-5ded69d510f1')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "  </svg>\n",
              "      </button>\n",
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              "      gap: 12px;\n",
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              "\n",
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              "\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",
              "    [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-71e9a8a0-67f7-498d-9891-5ded69d510f1 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-71e9a8a0-67f7-498d-9891-5ded69d510f1');\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",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "0 Prefix Assignment Tutorial Midterm TakeHome  Final\n",
              "0     05      57.14    34.09   64.38    51.48  52.50\n",
              "1     08      95.05   105.49   67.50    99.07  68.33\n",
              "2     08      83.70    83.17    30.0    63.15  48.89\n",
              "3     07      81.22    96.06   49.38   105.93  80.56\n",
              "4     08      91.32    93.64    95.0   107.41  73.89"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.info()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Tx6Z-d1vJ_He",
        "outputId": "46c2a4ac-6aed-4be2-a7f9-bfbef9ad6d2d"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 99 entries, 0 to 98\n",
            "Data columns (total 6 columns):\n",
            " #   Column      Non-Null Count  Dtype \n",
            "---  ------      --------------  ----- \n",
            " 0   Prefix      99 non-null     object\n",
            " 1   Assignment  99 non-null     object\n",
            " 2   Tutorial    99 non-null     object\n",
            " 3   Midterm     99 non-null     object\n",
            " 4   TakeHome    99 non-null     object\n",
            " 5   Final       99 non-null     object\n",
            "dtypes: object(6)\n",
            "memory usage: 4.8+ KB\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we found that all the columns are type of object but must be of numeric according to dataset.\n",
        " So we will convert the data type object to numeric."
      ],
      "metadata": {
        "id": "nThnYfANptHU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df['Prefix'] = pd.to_numeric(df['Prefix'])\n",
        "df['Assignment'] = pd.to_numeric(df['Assignment'])\n",
        "df['Tutorial'] = pd.to_numeric(df['Tutorial'])\n",
        "df['Midterm'] = pd.to_numeric(df['Midterm'])\n",
        "df['TakeHome'] = pd.to_numeric(df['TakeHome'])\n",
        "df['Final'] = pd.to_numeric(df['Final'])"
      ],
      "metadata": {
        "id": "EQ5PcT6rSrXG"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.info()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-daYP6DwTLoj",
        "outputId": "868a1908-b305-4efb-a6c8-950edebee48a"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 99 entries, 0 to 98\n",
            "Data columns (total 6 columns):\n",
            " #   Column      Non-Null Count  Dtype  \n",
            "---  ------      --------------  -----  \n",
            " 0   Prefix      99 non-null     int64  \n",
            " 1   Assignment  99 non-null     float64\n",
            " 2   Tutorial    99 non-null     float64\n",
            " 3   Midterm     99 non-null     float64\n",
            " 4   TakeHome    98 non-null     float64\n",
            " 5   Final       96 non-null     float64\n",
            "dtypes: float64(5), int64(1)\n",
            "memory usage: 4.8 KB\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Checking if dataset contains duplicate values..?"
      ],
      "metadata": {
        "id": "HEfVC4xxqI77"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dups = df.duplicated()\n",
        "print('Number of duplicate rows = %d' % (dups.sum()))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Lk5UhSrsqH3p",
        "outputId": "8019a1ea-14f7-4f57-f81e-4ccd6cd63455"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of duplicate rows = 0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "There are no duplicates"
      ],
      "metadata": {
        "id": "E4LGVAO1qdqu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Shape of Dataset\n",
        "print(\"Number of Instances: \",df.shape[0])\n",
        "print(\"Number of Attributes: \", df.shape[1])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dqsPe-6leH4o",
        "outputId": "4afce9b4-c89d-42be-e45e-97c8e464eb91"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of Instances:  99\n",
            "Number of Attributes:  6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Above code shows that dataset is of shape [99x6].\n",
        "it means, there are 99 rows and 6 columns"
      ],
      "metadata": {
        "id": "ZaQRUJL9qkCq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df.describe()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "kj9sKEic67W1",
        "outputId": "2f269803-1c53-4453-f154-31845ab19d76"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-5252b8c9-f3a2-4fec-b89c-9d536a78acb5\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        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></th>\n",
              "      <th>Prefix</th>\n",
              "      <th>Assignment</th>\n",
              "      <th>Tutorial</th>\n",
              "      <th>Midterm</th>\n",
              "      <th>TakeHome</th>\n",
              "      <th>Final</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>99.000000</td>\n",
              "      <td>99.000000</td>\n",
              "      <td>99.000000</td>\n",
              "      <td>99.000000</td>\n",
              "      <td>98.000000</td>\n",
              "      <td>96.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>7.313131</td>\n",
              "      <td>85.491717</td>\n",
              "      <td>89.731111</td>\n",
              "      <td>68.049495</td>\n",
              "      <td>80.828469</td>\n",
              "      <td>68.414375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>0.932918</td>\n",
              "      <td>12.597694</td>\n",
              "      <td>15.071556</td>\n",
              "      <td>19.376074</td>\n",
              "      <td>23.808806</td>\n",
              "      <td>18.801087</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>4.000000</td>\n",
              "      <td>28.140000</td>\n",
              "      <td>34.090000</td>\n",
              "      <td>28.120000</td>\n",
              "      <td>16.910000</td>\n",
              "      <td>28.060000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>7.000000</td>\n",
              "      <td>80.875000</td>\n",
              "      <td>83.350000</td>\n",
              "      <td>52.810000</td>\n",
              "      <td>66.015000</td>\n",
              "      <td>53.122500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>8.000000</td>\n",
              "      <td>89.940000</td>\n",
              "      <td>93.100000</td>\n",
              "      <td>69.380000</td>\n",
              "      <td>87.960000</td>\n",
              "      <td>66.250000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>8.000000</td>\n",
              "      <td>95.000000</td>\n",
              "      <td>100.550000</td>\n",
              "      <td>82.810000</td>\n",
              "      <td>98.747500</td>\n",
              "      <td>84.167500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>8.000000</td>\n",
              "      <td>100.830000</td>\n",
              "      <td>112.580000</td>\n",
              "      <td>110.000000</td>\n",
              "      <td>108.890000</td>\n",
              "      <td>108.890000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-5252b8c9-f3a2-4fec-b89c-9d536a78acb5')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\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",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\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",
              "    [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-5252b8c9-f3a2-4fec-b89c-9d536a78acb5 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-5252b8c9-f3a2-4fec-b89c-9d536a78acb5');\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",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "0         Prefix  Assignment    Tutorial     Midterm    TakeHome       Final\n",
              "count  99.000000   99.000000   99.000000   99.000000   98.000000   96.000000\n",
              "mean    7.313131   85.491717   89.731111   68.049495   80.828469   68.414375\n",
              "std     0.932918   12.597694   15.071556   19.376074   23.808806   18.801087\n",
              "min     4.000000   28.140000   34.090000   28.120000   16.910000   28.060000\n",
              "25%     7.000000   80.875000   83.350000   52.810000   66.015000   53.122500\n",
              "50%     8.000000   89.940000   93.100000   69.380000   87.960000   66.250000\n",
              "75%     8.000000   95.000000  100.550000   82.810000   98.747500   84.167500\n",
              "max     8.000000  100.830000  112.580000  110.000000  108.890000  108.890000"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"No. of missing values: \")\n",
        "for col in df.columns:\n",
        "  print('\\t%s: %d' % (col,df[col].isna().sum()))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R7pr79UBicft",
        "outputId": "a9a5590f-e710-455f-b25f-bb7eae81cf11"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "No. of missing values: \n",
            "\tPrefix: 0\n",
            "\tAssignment: 0\n",
            "\tTutorial: 0\n",
            "\tMidterm: 0\n",
            "\tTakeHome: 1\n",
            "\tFinal: 3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df['TakeHome'] = df['TakeHome'].fillna(df['TakeHome'].mean())"
      ],
      "metadata": {
        "id": "IDlgyE3sTgJm"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.Final = df.Final.fillna(df.Final.mean())"
      ],
      "metadata": {
        "id": "CCe_3WtpUDw1"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.TakeHome.isna().sum()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3qELu65kUcfn",
        "outputId": "bc408d78-fcc4-4458-bf69-2834b3444b48"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.Final.isna().sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M4j9bHq4UnGz",
        "outputId": "0d91f939-0fb2-4ed0-84c3-fa4f3afc52e1"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Outliers"
      ],
      "metadata": {
        "id": "PZKMl46QUmxU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df.head"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dbdlJGdtv59r",
        "outputId": "6547a32b-30d2-48f6-b64b-0daccaa11cc7"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<bound method NDFrame.head of 0   Prefix  Assignment  Tutorial  Midterm  TakeHome  Final\n",
              "0        5       57.14     34.09    64.38     51.48  52.50\n",
              "1        8       95.05    105.49    67.50     99.07  68.33\n",
              "2        8       83.70     83.17    30.00     63.15  48.89\n",
              "3        7       81.22     96.06    49.38    105.93  80.56\n",
              "4        8       91.32     93.64    95.00    107.41  73.89\n",
              "..     ...         ...       ...      ...       ...    ...\n",
              "94       8       96.73    103.71    45.00     93.52  61.94\n",
              "95       7       85.34     80.54    41.25     93.70  39.72\n",
              "96       8       89.94    102.77    87.50     90.74  87.78\n",
              "97       7       95.60     76.13    66.25     99.81  85.56\n",
              "98       8       63.40     97.37    73.12     72.78  77.22\n",
              "\n",
              "[99 rows x 6 columns]>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%matplotlib inline\n",
        "\n",
        "df.plot(kind ='box', figsize=(12,12), layout=(2,3), sharex = True, \n",
        "        subplots = True)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 822
        },
        "id": "jFctUUAlQBgx",
        "outputId": "c820a288-39d6-4277-b516-bd0aa0997cb7"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Prefix           AxesSubplot(0.125,0.536818;0.227941x0.343182)\n",
              "Assignment    AxesSubplot(0.398529,0.536818;0.227941x0.343182)\n",
              "Tutorial      AxesSubplot(0.672059,0.536818;0.227941x0.343182)\n",
              "Midterm             AxesSubplot(0.125,0.125;0.227941x0.343182)\n",
              "TakeHome         AxesSubplot(0.398529,0.125;0.227941x0.343182)\n",
              "Final            AxesSubplot(0.672059,0.125;0.227941x0.343182)\n",
              "dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x864 with 6 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Z- Score\n",
        "Z-score is basically tells that how far a point is from mean.\n",
        "\n",
        "\n",
        "To discard the outliers, we can compute the Z-score for each attribute and remove those instances containing attributes with abnormally high or low Z-score (e.g., if Z > 3 or Z <= -3).\n",
        "\n",
        "Code:\n",
        "\n",
        "The following code shows the results of standardizing the columns of the data. Note that missing values (NaN) are not affected by the standardization process."
      ],
      "metadata": {
        "id": "9muD7U0aWBQf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Z = (df-df.mean())/df.std()\n",
        "Z[0:5]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "8mI-xiOpVOVI",
        "outputId": "6404d22c-eff5-4cfd-95dd-c5d2512e664a"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-527052ae-5bce-44ea-8dcd-fd56471c9fa2\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        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></th>\n",
              "      <th>Prefix</th>\n",
              "      <th>Assignment</th>\n",
              "      <th>Tutorial</th>\n",
              "      <th>Midterm</th>\n",
              "      <th>TakeHome</th>\n",
              "      <th>Final</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-2.479458</td>\n",
              "      <td>-2.250548</td>\n",
              "      <td>-3.691796</td>\n",
              "      <td>-0.189383</td>\n",
              "      <td>-1.239011</td>\n",
              "      <td>-0.859722</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.736258</td>\n",
              "      <td>0.758733</td>\n",
              "      <td>1.045605</td>\n",
              "      <td>-0.028359</td>\n",
              "      <td>0.770107</td>\n",
              "      <td>-0.004558</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.736258</td>\n",
              "      <td>-0.142226</td>\n",
              "      <td>-0.435331</td>\n",
              "      <td>-1.963736</td>\n",
              "      <td>-0.746336</td>\n",
              "      <td>-1.054740</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.335647</td>\n",
              "      <td>-0.339087</td>\n",
              "      <td>0.419923</td>\n",
              "      <td>-0.963533</td>\n",
              "      <td>1.059717</td>\n",
              "      <td>0.656127</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.736258</td>\n",
              "      <td>0.462647</td>\n",
              "      <td>0.259355</td>\n",
              "      <td>1.390917</td>\n",
              "      <td>1.122198</td>\n",
              "      <td>0.295803</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-527052ae-5bce-44ea-8dcd-fd56471c9fa2')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\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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              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "    }\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",
              "    [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-527052ae-5bce-44ea-8dcd-fd56471c9fa2 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-527052ae-5bce-44ea-8dcd-fd56471c9fa2');\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",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "0    Prefix  Assignment  Tutorial   Midterm  TakeHome     Final\n",
              "0 -2.479458   -2.250548 -3.691796 -0.189383 -1.239011 -0.859722\n",
              "1  0.736258    0.758733  1.045605 -0.028359  0.770107 -0.004558\n",
              "2  0.736258   -0.142226 -0.435331 -1.963736 -0.746336 -1.054740\n",
              "3 -0.335647   -0.339087  0.419923 -0.963533  1.059717  0.656127\n",
              "4  0.736258    0.462647  0.259355  1.390917  1.122198  0.295803"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print('Number of rows before discarding outliers = %d' % (Z.shape[0]))\n",
        "\n",
        "Z2 = Z.loc[((Z > -3).sum(axis=1)==6) & ((Z <= 3).sum(axis=1)==6),:]\n",
        "print('Number of rows after discarding missing values = %d' % (Z2.shape[0]))"
      ],
      "metadata": {
        "id": "OmUVFHwiWUjo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "228264d8-4fab-45ab-b6d1-42b00316701f"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of rows before discarding outliers = 99\n",
            "Number of rows after discarding missing values = 93\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Sampling\n",
        "Sampling is an approach commonly used to facilitate (1) data reduction for exploratory data analysis and scaling up algorithms to big data applications and (2) quantifying uncertainties due to varying data distributions. There are various methods available for data sampling, such as sampling without replacement, where each selected instance is removed from the dataset, and sampling with replacement, where each selected instance is not removed, thus allowing it to be selected more than once in the sample."
      ],
      "metadata": {
        "id": "vRO7tfaTaWeW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "8hZ5K-3mZ9PG",
        "outputId": "97c2e791-16f7-4580-a17f-400ab92adb76"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
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              "      <div>\n",
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              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
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              "\n",
              "    .dataframe thead th {\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Prefix</th>\n",
              "      <th>Assignment</th>\n",
              "      <th>Tutorial</th>\n",
              "      <th>Midterm</th>\n",
              "      <th>TakeHome</th>\n",
              "      <th>Final</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5</td>\n",
              "      <td>57.14</td>\n",
              "      <td>34.09</td>\n",
              "      <td>64.38</td>\n",
              "      <td>51.48</td>\n",
              "      <td>52.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>95.05</td>\n",
              "      <td>105.49</td>\n",
              "      <td>67.50</td>\n",
              "      <td>99.07</td>\n",
              "      <td>68.33</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>8</td>\n",
              "      <td>83.70</td>\n",
              "      <td>83.17</td>\n",
              "      <td>30.00</td>\n",
              "      <td>63.15</td>\n",
              "      <td>48.89</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>7</td>\n",
              "      <td>81.22</td>\n",
              "      <td>96.06</td>\n",
              "      <td>49.38</td>\n",
              "      <td>105.93</td>\n",
              "      <td>80.56</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8</td>\n",
              "      <td>91.32</td>\n",
              "      <td>93.64</td>\n",
              "      <td>95.00</td>\n",
              "      <td>107.41</td>\n",
              "      <td>73.89</td>\n",
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              "  </svg>\n",
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              "      background-color: #E2EBFA;\n",
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              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "    }\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",
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              "  </style>\n",
              "\n",
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              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-f995bc59-2215-4ebd-9030-e3adfc678111');\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",
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              "  "
            ],
            "text/plain": [
              "0  Prefix  Assignment  Tutorial  Midterm  TakeHome  Final\n",
              "0       5       57.14     34.09    64.38     51.48  52.50\n",
              "1       8       95.05    105.49    67.50     99.07  68.33\n",
              "2       8       83.70     83.17    30.00     63.15  48.89\n",
              "3       7       81.22     96.06    49.38    105.93  80.56\n",
              "4       8       91.32     93.64    95.00    107.41  73.89"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the following code, a sample of size 3 is randomly selected (without replacement) from the original data."
      ],
      "metadata": {
        "id": "-8WaUe38bLqJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sample = df.sample(n=3)\n",
        "sample"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "HiNhBwNbagCs",
        "outputId": "e509f58e-8b45-436f-bbad-366169befe94"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
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              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "    <tr>\n",
              "      <th>93</th>\n",
              "      <td>8</td>\n",
              "      <td>87.52</td>\n",
              "      <td>91.58</td>\n",
              "      <td>56.25</td>\n",
              "      <td>71.85</td>\n",
              "      <td>85.00</td>\n",
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              "      <th>1</th>\n",
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              "    }\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-bdad3eb3-2bd6-4e91-a0b6-6a5fac36bf36 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-bdad3eb3-2bd6-4e91-a0b6-6a5fac36bf36');\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",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "0   Prefix  Assignment  Tutorial  Midterm  TakeHome  Final\n",
              "93       8       87.52     91.58    56.25     71.85  85.00\n",
              "1        8       95.05    105.49    67.50     99.07  68.33\n",
              "57       8       87.93    108.97    28.75     87.96  47.78"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the next example, we randomly select 1% of the data (without replacement) and display the selected samples. The random_state argument of the function specifies the seed value of the random number generator."
      ],
      "metadata": {
        "id": "81TL6HNJa3Bj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sample = df.sample(frac=0.01, random_state=1)\n",
        "sample"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "_Z87ALHEalpA",
        "outputId": "33008abc-01d9-446e-eb98-017283a06f48"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-65efb833-afd1-4030-9abf-f61c9296add2\">\n",
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              "<style scoped>\n",
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              "\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Prefix</th>\n",
              "      <th>Assignment</th>\n",
              "      <th>Tutorial</th>\n",
              "      <th>Midterm</th>\n",
              "      <th>TakeHome</th>\n",
              "      <th>Final</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>92</th>\n",
              "      <td>7</td>\n",
              "      <td>95.6</td>\n",
              "      <td>82.28</td>\n",
              "      <td>76.88</td>\n",
              "      <td>108.33</td>\n",
              "      <td>78.33</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-65efb833-afd1-4030-9abf-f61c9296add2')\"\n",
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              "      \n",
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              "      gap: 12px;\n",
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              "\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-65efb833-afd1-4030-9abf-f61c9296add2 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-65efb833-afd1-4030-9abf-f61c9296add2');\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",
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              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "0   Prefix  Assignment  Tutorial  Midterm  TakeHome  Final\n",
              "92       7        95.6     82.28    76.88    108.33  78.33"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, we perform a sampling with replacement to create a sample whose size is equal to 1% of the entire data. You should be able to observe duplicate instances in the sample by increasing the sample size."
      ],
      "metadata": {
        "id": "A5DCdQGea63W"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sample = df.sample(frac=0.01, replace=True, random_state=1)\n",
        "sample\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        },
        "id": "SeiZhMofavBD",
        "outputId": "c4d7f6fc-a60b-4490-9714-3e9882e676f8"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-228522fa-cf2b-4562-80eb-a6b8463e2ff0\">\n",
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              "\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Prefix</th>\n",
              "      <th>Assignment</th>\n",
              "      <th>Tutorial</th>\n",
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              "      <th>Final</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>37</th>\n",
              "      <td>7</td>\n",
              "      <td>89.89</td>\n",
              "      <td>57.97</td>\n",
              "      <td>32.5</td>\n",
              "      <td>85.19</td>\n",
              "      <td>51.67</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-228522fa-cf2b-4562-80eb-a6b8463e2ff0')\"\n",
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              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
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              "      border-radius: 50%;\n",
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              "      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",
              "    [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-228522fa-cf2b-4562-80eb-a6b8463e2ff0 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-228522fa-cf2b-4562-80eb-a6b8463e2ff0');\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",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "0   Prefix  Assignment  Tutorial  Midterm  TakeHome  Final\n",
              "37       7       89.89     57.97     32.5     85.19  51.67"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Discretization\n",
        "Discretization is a data preprocessing step that is often used to transform a continuous-valued attribute to a categorical attribute. The example below illustrates two simple but widely-used unsupervised discretization methods applied to the 'Assignment' attribute of the breast cancer dataset.\n",
        "\n",
        "First, we plot a histogram that shows the distribution of the attribute values. The value_counts() function can also be applied to count the frequency of each attribute value.\n",
        "\n"
      ],
      "metadata": {
        "id": "lYKlcB4Obcfu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df['Assignment'].hist(bins=10)\n",
        "df['Assignment'].value_counts(sort=False)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "j5LO2vlRbXFC",
        "outputId": "4620fd31-f91f-475f-9fd8-a8c4422a5e2b"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "57.14     2\n",
              "95.05     3\n",
              "83.70     2\n",
              "81.22     2\n",
              "91.32     2\n",
              "95.00     3\n",
              "72.85     2\n",
              "84.26     3\n",
              "90.10     1\n",
              "80.44     2\n",
              "86.26     3\n",
              "97.16     2\n",
              "91.28     3\n",
              "84.80     2\n",
              "93.83     3\n",
              "92.01     2\n",
              "55.14     1\n",
              "93.04     1\n",
              "63.40     2\n",
              "75.27     3\n",
              "63.78     1\n",
              "53.36     1\n",
              "82.45     1\n",
              "91.62     1\n",
              "98.58     3\n",
              "67.29     1\n",
              "85.42     1\n",
              "88.09     1\n",
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              "90.74     1\n",
              "28.14     1\n",
              "95.14     2\n",
              "68.95     2\n",
              "85.01     1\n",
              "95.90     1\n",
              "92.46     1\n",
              "96.73     2\n",
              "71.79     3\n",
              "87.93     3\n",
              "92.02     3\n",
              "90.33     1\n",
              "97.00     2\n",
              "93.01     1\n",
              "100.83    1\n",
              "80.53     1\n",
              "90.98     1\n",
              "93.59     1\n",
              "97.33     3\n",
              "66.17     1\n",
              "74.29     1\n",
              "86.86     1\n",
              "95.60     3\n",
              "98.49     1\n",
              "74.35     1\n",
              "86.29     1\n",
              "96.41     1\n",
              "87.52     1\n",
              "85.34     1\n",
              "89.94     1\n",
              "Name: Assignment, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 34
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "we can apply the cut() function to discretize the attribute into 4 bins of similar interval. The value_counts() function can be used to determine the number of instances in each bin."
      ],
      "metadata": {
        "id": "cUeHzq7PcTIh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "bins = pd.cut(df['Assignment'],4)\n",
        "bins.value_counts(sort=False)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BAi6lGDYcGI6",
        "outputId": "3364a394-be53-4a97-dd7a-42fd5090c254"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(28.067, 46.312]     1\n",
              "(46.312, 64.485]     7\n",
              "(64.485, 82.658]    20\n",
              "(82.658, 100.83]    71\n",
              "Name: Assignment, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "For the equal frequency method, the qcut() function can be used to partition the values into 4 bins such that each bin has nearly the same number of instances."
      ],
      "metadata": {
        "id": "Zo5th6Q7cj8e"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "bins = pd.qcut(df['Assignment'],4)\n",
        "bins.value_counts(sort=False)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dbiyKE9wcdF8",
        "outputId": "fcca07e2-0ce0-4fe6-c483-31ef3f55ecfe"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(28.139, 80.875]    25\n",
              "(80.875, 89.94]     25\n",
              "(89.94, 95.0]       25\n",
              "(95.0, 100.83]      24\n",
              "Name: Assignment, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#to check distribution of data\n",
        "Feature scaling is the method to limit the range of variables so that they can be compared on common grounds. \n",
        "It is performed on continuous variables. \n",
        "This is the  plot  for the distribution of all the continuous variables in  the data set.\n",
        "feature scaling to convert different scales to a standard scale \n",
        "\n"
      ],
      "metadata": {
        "id": "n7WXtkPDc00G"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "scaler = StandardScaler().fit(df)\n",
        "rescaledX = scaler.transform(df)\n",
        "print(rescaledX)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v0vdqF1scr9E",
        "outputId": "0b47c3e2-1576-4d69-ced3-e5a84a5d4eff"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-2.49207650e+00 -2.26200143e+00 -3.71058404e+00 -1.90346571e-01\n",
            "  -1.24531600e+00 -8.64096841e-01]\n",
            " [ 7.40005249e-01  7.62594001e-01  1.05092584e+00 -2.85037808e-02\n",
            "   7.74025713e-01 -4.58127768e-03]\n",
            " [ 7.40005249e-01 -1.42949606e-01 -4.37546154e-01 -1.97372963e+00\n",
            "  -7.50133866e-01 -1.06010765e+00]\n",
            " [-3.37355334e-01 -3.40812879e-01  4.22059762e-01 -9.68436911e-01\n",
            "   1.06510964e+00  6.59466438e-01]\n",
            " [ 7.40005249e-01  4.65001256e-01  2.60675253e-01  1.39799518e+00\n",
            "   1.12790909e+00  2.97307954e-01]\n",
            " [-3.37355334e-01  7.58604822e-01  1.89986171e-01  1.30047452e+00\n",
            "   7.19288357e-01 -1.92413662e-02]\n",
            " [ 7.40005249e-01  7.62594001e-01  8.84206309e-01 -6.12071536e-01\n",
            "   7.74025713e-01 -9.99838401e-01]\n",
            " [-3.37355334e-01 -1.00860142e+00 -1.92135000e-01 -4.17548951e-01\n",
            "   1.20599167e-15 -6.68086027e-01]\n",
            " [ 7.40005249e-01 -9.82708027e-02  2.24663834e-01 -1.06595757e+00\n",
            "  -2.64387668e+00 -9.54772203e-01]\n",
            " [-3.37355334e-01  3.67665291e-01  5.21424604e-01 -8.71434982e-01\n",
            "   3.42067347e-01 -2.60861344e-01]\n",
            " [-3.37355334e-01 -4.03044070e-01  3.12691748e-02  3.60541389e-01\n",
            "   4.51966381e-01 -1.55800770e+00]\n",
            " [-1.41471592e+00  6.12963527e-02 -6.08933834e-01  3.28380322e-01\n",
            "   2.86905670e-01  4.93318767e-01]\n",
            " [ 7.40005249e-01  9.30937350e-01  9.32221535e-01  2.30859666e-01\n",
            "   5.38527783e-01 -2.76064399e-01]\n",
            " [-3.37355334e-01  4.61809913e-01 -4.13538541e-01  6.84745697e-01\n",
            "   8.05425437e-01  1.29256508e+00]\n",
            " [ 7.40005249e-01 -5.51876707e-02 -4.34211763e-02 -1.22780036e+00\n",
            "  -2.71219230e+00 -1.76922157e+00]\n",
            " [-3.37355334e-01  6.65258036e-01  3.80046439e-01  1.04111107e+00\n",
            "   4.30815299e-03  1.17202657e+00]\n",
            " [ 7.40005249e-01 -5.51876707e-02 -4.34211763e-02 -1.06595757e+00\n",
            "  -2.71219230e+00 -8.19030642e-01]\n",
            " [-3.56943708e+00  5.20051925e-01  8.52863037e-01 -1.51984360e+00\n",
            "   2.24106221e-01 -1.04490460e+00]\n",
            " [ 7.40005249e-01 -2.42156859e+00 -5.25574068e-01  3.60541389e-01\n",
            "  -1.04885557e+00 -3.21130597e-01]\n",
            " [ 7.40005249e-01  6.02229010e-01 -4.53551229e-01  5.87743768e-01\n",
            "   1.06145096e-01  1.23229582e+00]\n",
            " [ 7.40005249e-01 -1.76255623e+00 -2.34815201e-01 -2.55706160e-01\n",
            "  -3.41513132e-01  7.71601440e-16]\n",
            " [ 7.40005249e-01 -8.15525166e-01  5.19423969e-01 -2.55706160e-01\n",
            "  -8.36695267e-01 -1.25119784e-01]\n",
            " [ 7.40005249e-01 -1.73223847e+00 -9.01693336e-01 -1.48716380e+00\n",
            "  -1.63823687e+00 -1.84469388e+00]\n",
            " [-3.37355334e-01 -4.03044070e-01  3.12691748e-02 -1.13079843e+00\n",
            "   4.51966381e-01  2.06632591e-01]\n",
            " [-3.37355334e-01 -2.56358335e+00 -5.14904017e-01  3.28380322e-01\n",
            "   9.23386563e-01 -6.52882972e-01]\n",
            " [-1.41471592e+00  4.61809913e-01  3.67375755e-01  7.49586559e-01\n",
            "   7.11226265e-01  1.32297119e+00]\n",
            " [ 7.40005249e-01 -2.42679078e-01 -2.05472563e-01  1.30047452e+00\n",
            "   2.00768589e-01  1.12696037e+00]\n",
            " [ 7.40005249e-01 -8.15525166e-01 -2.04138807e-01  6.90168751e-02\n",
            "  -8.36695267e-01  1.11175732e+00]\n",
            " [ 7.40005249e-01  4.65001256e-01  3.44035020e-01  4.25382251e-01\n",
            "   1.12790909e+00  9.30949559e-01]\n",
            " [-3.37355334e-01  4.88936329e-01 -1.63725992e+00  1.98698598e-01\n",
            "   3.89166933e-01 -1.24091541e+00]\n",
            " [-3.37355334e-01  1.04423003e+00  8.48861768e-01 -2.85037808e-02\n",
            "   7.11226265e-01 -2.76064399e-01]\n",
            " [-3.37355334e-01  6.12963527e-02 -7.74319612e-02  1.01177943e-01\n",
            "   2.86905670e-01 -7.28355280e-01]\n",
            " [ 7.40005249e-01 -1.45219812e+00  3.94050880e-01 -1.03379650e+00\n",
            "  -3.65275086e-01 -1.36199689e+00]\n",
            " [-3.37355334e-01  1.04423003e+00  8.66200599e-02  1.72219948e+00\n",
            "   9.94248102e-01  2.13742055e+00]\n",
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            "  -3.41513132e-01  4.78115713e-01]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "yHUJaGoUc-o8"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}