{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "600a8c26",
      "metadata": {
        "id": "600a8c26"
      },
      "source": [
        "\n",
        "\n",
        "# Introduction to Jupyter Notebook\n",
        "\n",
        "This is a brief introduction to how Jupyter Notebook (and Python) works using a few simple examples.\n",
        "\n",
        "A Jupyter Notebook file (i.e. a .ipynb file) consists of:\n",
        "\n",
        "- Simple text like this (LateX users can exploit common LateX formulas like $\\sqrt{9} = 3$ etc.).\n",
        "    + Headings are created by hashtags; a single hashtag is the largest level.\n",
        "- Code chunks where we execute Python commands.\n",
        "- Output where we display the result of the code chunks.\n",
        "\n",
        "A first peak at a code chunk:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "217e5ed2",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "217e5ed2",
        "outputId": "198833ae-4114-4fd9-a353-8adc65a1a7c6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "1+1"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e5d166f5",
      "metadata": {
        "id": "e5d166f5"
      },
      "source": [
        "\n",
        "The above chunk can be executed by hitting the \"play\" button in the left side of the chunk or simply placing the cursor at line with `1+1` and hit Ctrl+Enter (on Windows). The result is shown below the code.\n",
        "\n",
        "### Exercise:\n",
        "  - Run all the codes chunk by clicking \"Run all\" at the top. This will run all Python chunks consecutively (one after one).\n",
        "  - Insert a new code chunk by clicking \"+Code\".\n",
        "  - Once the chunk is inserted, calculate 1+2+3+4+5"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ed9cb81c",
      "metadata": {
        "id": "ed9cb81c"
      },
      "source": [
        "# Python\n",
        "\n",
        "## Python as a Calculator\n",
        "\n",
        "- **Python** can be used like a simple calculator:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "f5e71f83",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f5e71f83",
        "outputId": "1fae4895-c83a-428d-de28-83d1e339f768"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "-2"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "3-5"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "509b4491",
      "metadata": {
        "id": "509b4491"
      },
      "source": [
        "- If we do several commands at the same time, we only get the output of the last command. Using the print() function, we can print the output of all the commands."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "5da337ad",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5da337ad",
        "outputId": "8e068b6c-badd-4ec5-bfc6-b7a137f86017"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "27\n",
            "1.2\n",
            "9\n"
          ]
        }
      ],
      "source": [
        "print(3*9)\n",
        "print(6/5)\n",
        "print(3**2)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "bc9a4da0",
      "metadata": {
        "id": "bc9a4da0"
      },
      "source": [
        "- Not all standard mathematical functions are available in Python, but we can import additional packages to do so. The import command loads a package into Python: In this case we load the numpy (numerical python) package and give it the short name np. When loaded, we can calculate many standard mathematical functions by writing np.function_name."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "8aa55ac0",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8aa55ac0",
        "outputId": "dcba72f2-d6fd-4ae4-eb14-b76f8b9e3a3a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "3.0\n",
            "3.141592653589793\n",
            "4.605170185988092\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "\n",
        "print(np.sqrt(9))\n",
        "print(np.pi)\n",
        "print(np.log(100))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "17c2c2f1",
      "metadata": {
        "id": "17c2c2f1"
      },
      "source": [
        "\n",
        "# Using Add-on Packages\n",
        "Since we have now begun using extra packages in Python, we will have a brief introduction to using those. Python has a lot of functionality by itself, but nonetheless we will not get very far without loading additional packages.\n",
        "\n",
        "If you are using Google Colab, most of the common packages are already installed. If you are using a local installation, such as VS-code, you will need to install them. Either way once they are installed, you still need to load them, before they can be used. This is usually done in the top of the document, but can be done at any point before it is used. For this document, we need the following packages:\n",
        "- numpy (for numerical calculations),\n",
        "- pandas (for handling data),\n",
        "- matplotlib and seaborn (for plotting)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "dff1fd78",
      "metadata": {
        "id": "dff1fd78"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ZL-TZ7e22Ak-",
      "metadata": {
        "id": "ZL-TZ7e22Ak-"
      },
      "source": [
        "We have already loaded numpy, so we do not really need to do this again, but it is good practice to load all packages together (at the top of the document).\n",
        "\n",
        "Now that we have loaded the packages, we can use these further down in the document. Note that whenever we use a function from a package, we need to use the package name (or rather, the short version) followed by a period and then the function name. For example, we used the function `sqrt` from the `np` package by typing `np.sqrt` above. Note that if you close and reopen the notebook, you will need to run the code again to load the packages (for example, press the button `Run All` to make sure everything is loaded)."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "401ca417",
      "metadata": {
        "id": "401ca417"
      },
      "source": [
        "## Variable Assignment\n",
        "\n",
        "- We can assign a value to a variable using the assignment operator `=`.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "fcd6a03e",
      "metadata": {
        "id": "fcd6a03e"
      },
      "outputs": [],
      "source": [
        "a = 99\n",
        "b = 1"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "468a7cd9",
      "metadata": {
        "id": "468a7cd9"
      },
      "source": [
        "- We can now work with these variables in subsequent chunks:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "749f3639",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "749f3639",
        "outputId": "e90d8da9-a09f-4f05-ce6a-3e0bf0732685"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "100"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a+b"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "eef5dcd8",
      "metadata": {
        "id": "eef5dcd8"
      },
      "source": [
        "- There are some restriction when assigning. For example the name of a variable can not start with a number.\n",
        "- For longer names it is good practice to separate words with an underscore or using capital letters like: `mean_of_men_height` or `meanOfMenHeight`. However, such a long name for a mean value is probably overkill.\n",
        "- Meaningful names make your code easier for others to read, but also for yourself if you have to read your code again next month.\n",
        "- Make sure not to use \"old\" variable names (if a variable name is reused for a different value in the same document, be cautious!)\n",
        "- In code chunks, hashtags `#` allow comments and can be useful in reminding oneself of specific **Python** code (i.e. what the code does)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "id": "fcee7b2c",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fcee7b2c",
        "outputId": "5f075db1-dbff-4df4-aa63-59dc66774f20"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a\n",
        "b # This will only print b in the output"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8fca260f",
      "metadata": {
        "id": "8fca260f"
      },
      "source": [
        "### Exercise:\n",
        "- Create the variables $x$ and $y$ and assign the value 23 to $x$ and 11 to $y$ and try to add these together by writing $x+y$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "2be58063",
      "metadata": {
        "id": "2be58063"
      },
      "outputs": [],
      "source": [
        "# x = ...\n",
        "# y = ...\n",
        "# x + y"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "544604bb",
      "metadata": {
        "id": "544604bb"
      },
      "source": [
        "\n",
        "\n",
        "- Take the square root of y\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "21ced091",
      "metadata": {
        "id": "21ced091"
      },
      "outputs": [],
      "source": [
        "# np.sqrt(...)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "18d19c20",
      "metadata": {
        "id": "18d19c20"
      },
      "source": [
        "\n",
        "\n",
        "- Divide x by y\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "id": "78c510d5",
      "metadata": {
        "id": "78c510d5"
      },
      "outputs": [],
      "source": [
        "# ... / ..."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5bdecc5a",
      "metadata": {
        "id": "5bdecc5a"
      },
      "source": [
        "# Data Structures\n",
        "A basic data structure in Python is the list which can be created using the `[a,b,c,...]`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "82e6aa69",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "82e6aa69",
        "outputId": "5a4b73db-58ac-488c-985a-edc8abe0c448"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[1.3, 5, 3.5, 7]\n"
          ]
        }
      ],
      "source": [
        "v = [1.3, 5, 3.5, 7]\n",
        "print(v)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "71fbe26f",
      "metadata": {
        "id": "71fbe26f"
      },
      "source": [
        "- We can access the elements of a list using the `v[i]`, where i is the number of the entry we want to access. Note that Python enumerates from 0, not 1."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "id": "80b5243e",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "80b5243e",
        "outputId": "52b73d5e-a3ee-4d2e-e591-853931a26597"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "5.4"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "\n",
        "v = [2.1, 4.2, 3.3, 5.4, 7]\n",
        "v[3] # Accessing the fourth element in v"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d0f3e7fb",
      "metadata": {
        "id": "d0f3e7fb"
      },
      "source": [
        "- We can change elements in a list using subsetting:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "08fa04f9",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "08fa04f9",
        "outputId": "7b4a520d-7d78-43d8-cd87-5c74e7eeccfa"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[1, 0, 3]"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "v2 = [1, 2, 3]\n",
        "v2[1] = 0\n",
        "v2"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d22e935e",
      "metadata": {
        "id": "d22e935e"
      },
      "source": [
        "- A warning: The list is simple, and good for storing things, but it is not particularly useful if we want to do mathematical calculations. For example, writing + does not add the elements of the vectors together."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "id": "9a7eb420",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9a7eb420",
        "outputId": "8755d3aa-aac4-40c3-e60f-11b9aecd3f7e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[1, 2, 3, 4, 5, 6]"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "v3 = [1, 2, 3]\n",
        "v4 = [4, 5, 6]\n",
        "v3 + v4  # This concatenates the two lists"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "43b20645",
      "metadata": {
        "id": "43b20645"
      },
      "source": [
        "- If we want a more powerful data structure, we can use NumPy arrays. They allow for mathematical operations on the entire array. A few examples:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "id": "1570c828",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1570c828",
        "outputId": "593e4b30-7819-4d61-bfcd-f94b7000cf0a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[5 7 9]\n",
            "[1.         1.41421356 1.73205081]\n",
            "[1 4 9]\n",
            "6\n"
          ]
        }
      ],
      "source": [
        "v3 = np.array([1, 2, 3])\n",
        "v4 = np.array([4, 5, 6])\n",
        "\n",
        "print(v3 + v4) # now we add the two arrays element-wise\n",
        "print(np.sqrt(v3)) # square root of each element in v3\n",
        "print(v3**2) # squaring each element in v3\n",
        "print(sum(v3)) # sum of all elements in v3"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d5d4be8b",
      "metadata": {
        "id": "d5d4be8b"
      },
      "source": [
        "### Exercise\n",
        "- Calculate the sum of the numbers $1,2,3,4,5,6,7,8,9,10$\n",
        "- Square the numbers $1,2,3,4,5,6,7,8,9,10$, and calculate the sum of the squares of the numbers."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0763f987",
      "metadata": {
        "id": "0763f987"
      },
      "source": [
        "# Reading Data\n",
        "We shall now consider a specific dataset called `BrainSize`. We load it into Python using the `read_csv` function from the `pandas` package. This package is a very useful tool for working with data in Python."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "id": "ee4174d1",
      "metadata": {
        "id": "ee4174d1"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "\n",
        "BrainSize = pd.read_csv(\"https://asta.math.aau.dk/datasets?file=BrainSize.txt\", sep=\"\\t\")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fbf5f9e5",
      "metadata": {
        "id": "fbf5f9e5"
      },
      "source": [
        "\n",
        "\n",
        "The `BrainSize` dataset is now of a form called a data frame in R; you can think of it as an excel sheet with variables as columns.\n",
        "\n",
        "## Dataframes\n",
        "To get an overview (the first five rows) of a data frame you can use `.head`:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "id": "d23c2e82",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "d23c2e82",
        "outputId": "a53fab6c-5c00-45e2-de10-6e82cfc6964a"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<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>Gender</th>\n",
              "      <th>FSIQ</th>\n",
              "      <th>VIQ</th>\n",
              "      <th>PIQ</th>\n",
              "      <th>Weight</th>\n",
              "      <th>Height</th>\n",
              "      <th>MRI_Count</th>\n",
              "      <th>HeightIntervals</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Female</td>\n",
              "      <td>133</td>\n",
              "      <td>132</td>\n",
              "      <td>124</td>\n",
              "      <td>118</td>\n",
              "      <td>64.5</td>\n",
              "      <td>816932</td>\n",
              "      <td>(62,65]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Male</td>\n",
              "      <td>139</td>\n",
              "      <td>123</td>\n",
              "      <td>150</td>\n",
              "      <td>143</td>\n",
              "      <td>73.3</td>\n",
              "      <td>1038437</td>\n",
              "      <td>(71,74]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Male</td>\n",
              "      <td>133</td>\n",
              "      <td>129</td>\n",
              "      <td>128</td>\n",
              "      <td>172</td>\n",
              "      <td>68.8</td>\n",
              "      <td>965353</td>\n",
              "      <td>(68,71]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Female</td>\n",
              "      <td>137</td>\n",
              "      <td>132</td>\n",
              "      <td>134</td>\n",
              "      <td>147</td>\n",
              "      <td>65.0</td>\n",
              "      <td>951545</td>\n",
              "      <td>(62,65]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Female</td>\n",
              "      <td>99</td>\n",
              "      <td>90</td>\n",
              "      <td>110</td>\n",
              "      <td>146</td>\n",
              "      <td>69.0</td>\n",
              "      <td>928799</td>\n",
              "      <td>(68,71]</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Gender  FSIQ  VIQ  PIQ  Weight  Height  MRI_Count HeightIntervals\n",
              "0  Female   133  132  124     118    64.5     816932         (62,65]\n",
              "1    Male   139  123  150     143    73.3    1038437         (71,74]\n",
              "2    Male   133  129  128     172    68.8     965353         (68,71]\n",
              "3  Female   137  132  134     147    65.0     951545         (62,65]\n",
              "4  Female    99   90  110     146    69.0     928799         (68,71]"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "BrainSize.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4513684a",
      "metadata": {
        "id": "4513684a"
      },
      "source": [
        "\n",
        "We see that the `BrainSize` dataset consists of 7 columns:\n",
        "\n",
        "- `Gender`\n",
        "- `FSIQ`\n",
        "- `VIQ`\n",
        "- `PIQ`\n",
        "- `Weight`\n",
        "- `Height`\n",
        "- `MRI_Count`\n",
        "- `HeightIntervals`: The Height variable divided into 5 intervals\n",
        "\n",
        "We can extract columns from a data frame with the `[]` operator using the name of the column. For example, to extract the `Height` column, and calculate its average, we can use the following code:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "id": "6933b6ea",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6933b6ea",
        "outputId": "d9bf054e-9392-4384-e3c3-0ad58e4f5440"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "68.42105263157895\n"
          ]
        }
      ],
      "source": [
        "height = BrainSize['Height']\n",
        "print(height.mean())"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0d1e9864",
      "metadata": {
        "id": "0d1e9864"
      },
      "source": [
        "## Tabulate\n",
        "Recall the `BrainSize` data which we have already loaded into Python (using the pandas package). Now we can summarize the variable, for example counting the number of people of each gender:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "id": "f83d7d6d",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 178
        },
        "id": "f83d7d6d",
        "outputId": "3cd9c8ef-3fb6-4387-c23d-ffa83a76cb3a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Gender\n",
              "Female    20\n",
              "Male      18\n",
              "Name: count, dtype: int64"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "BrainSize['Gender'].value_counts()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "183fde31",
      "metadata": {
        "id": "183fde31"
      },
      "source": [
        "\n",
        "\n",
        "What we see is, that in this data set $20$ observations are Females and $18$ observations are Males. We can also make a cross tabulation of `Gender` and `HeightIntervals` (remember that HeightIntervals is a categorical variable with five levels):\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "id": "86f26d36",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "86f26d36",
        "outputId": "e19ebfb4-e45f-437a-b864-f6c3917e0dd8"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
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              "    }\n",
              "\n",
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              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>HeightIntervals</th>\n",
              "      <th>(62,65]</th>\n",
              "      <th>(65,68]</th>\n",
              "      <th>(68,71]</th>\n",
              "      <th>(71,74]</th>\n",
              "      <th>(74,77]</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Gender</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>Female</th>\n",
              "      <td>9</td>\n",
              "      <td>8</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Male</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>7</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "HeightIntervals  (62,65]  (65,68]  (68,71]  (71,74]  (74,77]\n",
              "Gender                                                      \n",
              "Female                 9        8        3        0        0\n",
              "Male                   0        3        7        4        4"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.crosstab(BrainSize['Gender'], BrainSize['HeightIntervals'])"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b2ae6dc1",
      "metadata": {
        "id": "b2ae6dc1"
      },
      "source": [
        "\n",
        "With this command we simply count `Gender` and `HeightIntervals` together. We see, that males are in general higher than females (for this data set).\n",
        "- To swap rows and columns in the cross tabulation, simply swap the variables in the command.\n",
        "- To get the relative frequencies (of the total observations) add `normalize='all'`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "id": "0d591f5b",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "0d591f5b",
        "outputId": "3f4558ef-5111-44fd-d8cf-535e19697468"
      },
      "outputs": [
        {
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            "text/html": [
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              "\n",
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              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>HeightIntervals</th>\n",
              "      <th>(62,65]</th>\n",
              "      <th>(65,68]</th>\n",
              "      <th>(68,71]</th>\n",
              "      <th>(71,74]</th>\n",
              "      <th>(74,77]</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Gender</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>Female</th>\n",
              "      <td>0.236842</td>\n",
              "      <td>0.210526</td>\n",
              "      <td>0.078947</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Male</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.078947</td>\n",
              "      <td>0.184211</td>\n",
              "      <td>0.105263</td>\n",
              "      <td>0.105263</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "HeightIntervals   (62,65]   (65,68]   (68,71]   (71,74]   (74,77]\n",
              "Gender                                                           \n",
              "Female           0.236842  0.210526  0.078947  0.000000  0.000000\n",
              "Male             0.000000  0.078947  0.184211  0.105263  0.105263"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.crosstab(BrainSize['Gender'], BrainSize['HeightIntervals'], normalize='all')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "afb423dd",
      "metadata": {
        "id": "afb423dd"
      },
      "source": [
        "\n",
        "\n",
        "There is also an option to add totals in the \"margins\" of the table:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "id": "a6423c44",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "a6423c44",
        "outputId": "3574dd45-fdbb-416c-fd6e-3149bdce22e8"
      },
      "outputs": [
        {
          "data": {
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              "\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>HeightIntervals</th>\n",
              "      <th>(62,65]</th>\n",
              "      <th>(65,68]</th>\n",
              "      <th>(68,71]</th>\n",
              "      <th>(71,74]</th>\n",
              "      <th>(74,77]</th>\n",
              "      <th>All</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Gender</th>\n",
              "      <th></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>Female</th>\n",
              "      <td>9</td>\n",
              "      <td>8</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Male</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>7</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>18</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>All</th>\n",
              "      <td>9</td>\n",
              "      <td>11</td>\n",
              "      <td>10</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>38</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "HeightIntervals  (62,65]  (65,68]  (68,71]  (71,74]  (74,77]  All\n",
              "Gender                                                           \n",
              "Female                 9        8        3        0        0   20\n",
              "Male                   0        3        7        4        4   18\n",
              "All                    9       11       10        4        4   38"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.crosstab(BrainSize['Gender'], BrainSize['HeightIntervals'], margins=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8d69baf6",
      "metadata": {
        "id": "8d69baf6"
      },
      "source": [
        "To get relative frequencies for each gender we use normalize='index' :"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "id": "4861c189",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 175
        },
        "id": "4861c189",
        "outputId": "1d05a829-1db7-4b3f-d34d-d4cb1b08e431"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
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              "    }\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>HeightIntervals</th>\n",
              "      <th>(62,65]</th>\n",
              "      <th>(65,68]</th>\n",
              "      <th>(68,71]</th>\n",
              "      <th>(71,74]</th>\n",
              "      <th>(74,77]</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Gender</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>Female</th>\n",
              "      <td>0.450000</td>\n",
              "      <td>0.400000</td>\n",
              "      <td>0.150000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Male</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.166667</td>\n",
              "      <td>0.388889</td>\n",
              "      <td>0.222222</td>\n",
              "      <td>0.222222</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>All</th>\n",
              "      <td>0.236842</td>\n",
              "      <td>0.289474</td>\n",
              "      <td>0.263158</td>\n",
              "      <td>0.105263</td>\n",
              "      <td>0.105263</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "HeightIntervals   (62,65]   (65,68]   (68,71]   (71,74]   (74,77]\n",
              "Gender                                                           \n",
              "Female           0.450000  0.400000  0.150000  0.000000  0.000000\n",
              "Male             0.000000  0.166667  0.388889  0.222222  0.222222\n",
              "All              0.236842  0.289474  0.263158  0.105263  0.105263"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.crosstab(BrainSize['Gender'], BrainSize['HeightIntervals'], margins=True,normalize='index')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "59b5fc47",
      "metadata": {
        "id": "59b5fc47"
      },
      "source": [
        "## Numerical summaries\n",
        "We can also summarize the `Height` for each `Gender` numerically using various numerical summaries (groupby('Gender') splits the data into the two genders here):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "id": "9286aacb",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9286aacb",
        "outputId": "e9470464-6666-4971-f1bb-6ef9f819a077"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "        count       mean       std   min    25%    50%     75%   max\n",
            "Gender                                                              \n",
            "Female   20.0  65.765000  2.288248  62.0  64.50  66.00  66.875  70.5\n",
            "Male     18.0  71.372222  3.367807  66.3  68.85  70.25  73.875  77.0\n"
          ]
        }
      ],
      "source": [
        "summary = BrainSize.groupby('Gender')['Height'].describe()\n",
        "print(summary)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0d816594",
      "metadata": {
        "id": "0d816594"
      },
      "source": [
        "As we have already guessed, the mean height of men is larger than the mean of women height.\n",
        "\n",
        "If we just want the mean height for each gender, we can do the following:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "id": "639717fd",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 178
        },
        "id": "639717fd",
        "outputId": "d72dca35-844f-4692-89b3-dbaf0fb94e3d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Gender\n",
              "Female    65.765000\n",
              "Male      71.372222\n",
              "Name: Height, dtype: float64"
            ]
          },
          "execution_count": 27,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "BrainSize.groupby('Gender')['Height'].mean()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e642d9b3",
      "metadata": {
        "id": "e642d9b3"
      },
      "source": [
        "### Exercises\n",
        "\n",
        "Consider the BrainSize data.\n",
        "\n",
        "- What is the mean value of the Weight variable?\n",
        "- What is the mean value of the Weight variable for each group of the Gender variable?"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e9079497",
      "metadata": {
        "id": "e9079497"
      },
      "source": [
        "## Visualizing Data\n",
        "\n",
        "For making nice plots in Python, we use the following two packages:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "id": "77a4e83e",
      "metadata": {
        "id": "77a4e83e"
      },
      "outputs": [],
      "source": [
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b91d3333",
      "metadata": {
        "id": "b91d3333"
      },
      "source": [
        "### Boxplots\n",
        "\n",
        "We can make boxplots for the height split by gender. The command plt.show() is used to show the plot."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "id": "19be204f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "19be204f",
        "outputId": "47987120-9aec-4b99-fb87-30c72fdcff7b"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "sns.boxplot(x='Gender', y='Height', data=BrainSize)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cc0ddf3c",
      "metadata": {
        "id": "cc0ddf3c"
      },
      "source": [
        "Or for weight split into the five height groups."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "id": "6513d964",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "6513d964",
        "outputId": "428268e1-6fb8-4ae1-eb3f-aa2d0b7396c8"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "sns.boxplot(x='HeightIntervals', y='Weight', data=BrainSize)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8df10ba0",
      "metadata": {
        "id": "8df10ba0"
      },
      "source": [
        "### Exercises\n",
        "\n",
        "Consider the BrainSize data.\n",
        "- Use the function `scatterplot` from `seaborn` to plot `Weight` against `Height` with a different color for each `Gender` (fill in the missing code)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "id": "aa81cd89",
      "metadata": {
        "id": "aa81cd89"
      },
      "outputs": [],
      "source": [
        "#sns.scatterplot(x=...,y=...,hue='Gender',data=BrainSize)\n",
        "#plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b033acee",
      "metadata": {
        "id": "b033acee"
      },
      "source": [
        "\n",
        "\n",
        "- Do the same, but with separate plots for males and females (fill in the missing code). The easiest way to do this is to use relplot, instead of scatterplot.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "id": "081730ea",
      "metadata": {
        "id": "081730ea"
      },
      "outputs": [],
      "source": [
        "#sns.relplot(x=..., y=..., col='Gender', data=BrainSize, kind='scatter')\n",
        "#plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ddb6d912",
      "metadata": {
        "id": "ddb6d912"
      },
      "source": [
        "\n",
        "\n",
        "- Do you see a different picture for males and females?\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.12"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}