{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IntroStat Week 1 Python\n",
    "\n",
    "Welcome to the first lecture in IntroStat\n",
    "\n",
    "During the lectures we will present both slides and notebooks. \n",
    "\n",
    "This is the notebook used in the lecture in week 1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First steps using python code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Addition\n",
    "2+3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a variable\n",
    "x = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# print out the value of the variable\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(type(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# try changing x to 3.8 and see what happens to the type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how jupyter notebooks work in two **modes**: **command** mode and **edit** mode. <br>\n",
    "\n",
    "To enter command mode press **esc** <br>\n",
    "\n",
    "To enter edit mode press **enter** <br>\n",
    "\n",
    "(you can also use the mouse/clicking for most tasks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a variable of the data-type \"list\", which can contain several values\n",
    "x = [1,4,6,2] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(type(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lists can contain many different types of data\n",
    "x = [1,4,'hello',0.232] \n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# what happens if we multiply a list by a number?\n",
    "print(x*5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# what if we had chosen a non-integer number?\n",
    "print(x*1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In conclusion: lists do not behave as vectors. <br>\n",
    "For example multiplication does not operate elementwise. <br> \n",
    "We want to work with a variable type that behave more like a vector (or matrix)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using Numpy for vectors (ndarrays)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "### import the NUMPY package for vectors (ndarray data type for multidimentional arrays), math functions, etc.\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# store data of student height in variable x (which is now an array, not a list)\n",
    "x = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[168 161 167 179 184 166 198 187 191 179]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "print(type(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# type is 'numpy.ndarray' - stands for n-dimensional array (1D = vector, 2D = matrix, etc.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "178.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate mean of x (average height of students)\n",
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "178.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# \"mean()\" can also be called as a method\n",
    "x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Have a look in the online documentation: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html\n",
    "\n",
    "The datatype \"ndarray\" (also called a numpy array) has many methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "161"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lets try some other \"methods\"\n",
    "x.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "198"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "149.11111111111111"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# what about variance? \n",
    "# OBS: need to remember ddof = 1 if you want to calculate the \"sample variance\"\n",
    "x.var(ddof=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ddof?? look in documentation for explanation: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.211106056009468"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# standard deviation (also remember ddof=1 for \"sample standard deviation\")\n",
    "x.std(ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'median'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[24], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;66;03m# what about the median?\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m x\u001b[38;5;241m.\u001b[39mmedian()\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'median'"
     ]
    }
   ],
   "source": [
    "# what about the median?\n",
    "x.median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "no method called median? \n",
    "\n",
    "OK, then we call the median() function directly from numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "179.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([163.5, 166.5, 179. , 189. , 194.5])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can also get other percentiles (50th percentile is the same as the median)\n",
    "np.percentile(x, [10,20,50,80,90], method='averaged_inverted_cdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[161 166 167 168 179 179 184 187 191 198]\n"
     ]
    }
   ],
   "source": [
    "# compare with sorted data\n",
    "x.sort()\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the method=\"averaged inverted cdf\"  <br>\n",
    "\n",
    "There are many different ways to define percentiles!\n",
    "\n",
    "See the documentaion: https://numpy.org/doc/stable/reference/generated/numpy.percentile.html#numpy.percentile\n",
    "\n",
    "In this course (and in the book) we use the 'averaged_inverted_cdf' method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now lets make some plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the matplotlib.pyplot package \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[161 166 167 168 179 179 184 187 191 198]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a histogram\n",
    "plt.hist(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Customize your histogram\n",
    "plt.hist(x, bins=8, edgecolor='black', color='red', alpha=0.7, density=True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Density')\n",
    "plt.title('Histogram Example')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k7e2t48eP82OoAAA0ERfz32+nHQEqLy9XTk6OwsLC/leMi4vCwsKUnZ3tcJ3s7Gy7+ZIUHh5um19ZWan33ntPV1xxhcLDw9W5c2cFBwcrLS2t3voAAABNTwtnvXBxcbEqKirk6+trN+7r66sdO3Y4XCc/P9/h/Pz8fElSYWGhTp48qfnz5+uJJ57QggULlJ6ernHjxmndunUKDQ11uN2ysjKVlZXZnpeUlFxKa6ZXVFTUrN9DLy8vderUydllAAAugdMCUH2orKyUJI0dO1YPPvigJCkoKEhZWVlKTU2tNgAlJSVp7ty5DVZnc1ZUVKT77rhDZUeOOLuUeuPesaOWrVxJCAKAJsxpAcjHx0eurq4qKCiwGy8oKJDVanW4jtVqPe98Hx8ftWjRQv3797eb069fP33++efV1pKQkKC4uDjb85KSEvn7+19UP/hZSUmJyo4c0UPu7vJv1crZ5dS5A6dPa+GRIyopKSEAAUAT5rQA5ObmpiFDhigzM1ORkZGSfj6Ck5mZqdjYWIfrhISEKDMzUzNmzLCNZWRkKCQkxLbNYcOGaefOnXbr7dq1Sz169Ki2Fnd3d7m7u19aQ7Dj36qVenl6OruM+vGL06UAgKbJqafA4uLiNGnSJA0dOlTDhw9XSkqKSktLFRMTI0maOHGiunbtqqSkJEnS9OnTFRoaqoULF2r06NFatWqVNm3apOXLl9u2GR8fr/Hjx2vUqFG69tprlZ6erv/85z9av369M1oEAACNkFMD0Pjx41VUVKTExETl5+crKChI6enptgud8/Ly5OLyvxvVRowYoZUrV2rWrFmaOXOm+vTpo7S0NA0cONA25+abb1ZqaqqSkpI0bdo09e3bV//61780cuTIBu8PAAA0Tk79HqDGiu8Bqr29e/dqRlSUUtq1a5anwPaWlmrGsWNKWb1avXr1cnY5AIBfaBLfAwQAAOAsBCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6jSIALV26VD179pSHh4eCg4O1cePG885fvXq1AgIC5OHhoUGDBmnt2rV2y6Ojo2WxWOweERER9dkCAABoQpwegN58803FxcVp9uzZys3NVWBgoMLDw1VYWOhwflZWliZMmKDJkydr8+bNioyMVGRkpLZv3243LyIiQocPH7Y9/vGPfzREOwAAoAlwegBKTk7WlClTFBMTo/79+ys1NVWtW7fWihUrHM5fvHixIiIiFB8fr379+mnevHkaPHiwlixZYjfP3d1dVqvV9mjfvn1DtAMAAJoApwag8vJy5eTkKCwszDbm4uKisLAwZWdnO1wnOzvbbr4khYeHV5m/fv16de7cWX379tV9992nI0eOVFtHWVmZSkpK7B4AAKD5cmoAKi4uVkVFhXx9fe3GfX19lZ+f73Cd/Pz8C86PiIjQq6++qszMTC1YsECffPKJbrzxRlVUVDjcZlJSkry9vW0Pf3//S+wMAAA0Zi2cXUB9uP32223/PmjQIF155ZXq1auX1q9fr+uvv77K/ISEBMXFxdmel5SUEIIAAGjGnHoEyMfHR66uriooKLAbLygokNVqdbiO1Wq9qPmSdPnll8vHx0d79uxxuNzd3V1eXl52DwAA0Hw5NQC5ublpyJAhyszMtI1VVlYqMzNTISEhDtcJCQmxmy9JGRkZ1c6XpB9++EFHjhxRly5d6qZwAADQpDn9LrC4uDg9//zzeuWVV/Ttt9/qvvvuU2lpqWJiYiRJEydOVEJCgm3+9OnTlZ6eroULF2rHjh2aM2eONm3apNjYWEnSyZMnFR8fry+++EL79u1TZmamxo4dq969eys8PNwpPQIAgMbF6dcAjR8/XkVFRUpMTFR+fr6CgoKUnp5uu9A5Ly9PLi7/y2kjRozQypUrNWvWLM2cOVN9+vRRWlqaBg4cKElydXXV1q1b9corr+jYsWPy8/PTDTfcoHnz5snd3d0pPQIAgMbFYhiG4ewiGpuSkhJ5e3vr+PHjXA90kfbu3asZUVFKaddOvTw9nV1OndtbWqoZx44pZfVq9erVy9nlAAB+4WL+++30U2AAAAANjQAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMhwAEAABMp1EEoKVLl6pnz57y8PBQcHCwNm7ceN75q1evVkBAgDw8PDRo0CCtXbu22rn33nuvLBaLUlJS6rhqAADQVDk9AL355puKi4vT7NmzlZubq8DAQIWHh6uwsNDh/KysLE2YMEGTJ0/W5s2bFRkZqcjISG3fvr3K3H//+9/64osv5OfnV99tAACAJsTpASg5OVlTpkxRTEyM+vfvr9TUVLVu3VorVqxwOH/x4sWKiIhQfHy8+vXrp3nz5mnw4MFasmSJ3byDBw/qgQce0BtvvKGWLVs2RCsAAKCJaOHMFy8vL1dOTo4SEhJsYy4uLgoLC1N2drbDdbKzsxUXF2c3Fh4errS0NNvzyspK3XXXXYqPj9eAAQMuWEdZWZnKyspsz0tKSi6yE6B5KSoqatafAy8vL3Xq1MnZZQBwIqcGoOLiYlVUVMjX19du3NfXVzt27HC4Tn5+vsP5+fn5tucLFixQixYtNG3atBrVkZSUpLlz515k9UDzVFRUpPvuuENlR444u5R6496xo5atXEkIAkzMqQGoPuTk5Gjx4sXKzc2VxWKp0ToJCQl2R5VKSkrk7+9fXyUCjVpJSYnKjhzRQ+7u8m/Vytnl1LkDp09r4ZEjKikpIQABJubUAOTj4yNXV1cVFBTYjRcUFMhqtTpcx2q1nnf+Z599psLCQnXv3t22vKKiQg899JBSUlK0b9++Ktt0d3eXu7v7JXYDNC/+rVqpl6ens8uoH7845Q3AnJx6EbSbm5uGDBmizMxM21hlZaUyMzMVEhLicJ2QkBC7+ZKUkZFhm3/XXXdp69at2rJli+3h5+en+Ph4ffDBB/XXDAAAaDKcfgosLi5OkyZN0tChQzV8+HClpKSotLRUMTExkqSJEyeqa9euSkpKkiRNnz5doaGhWrhwoUaPHq1Vq1Zp06ZNWr58uSSpY8eO6tixo91rtGzZUlarVX379m3Y5gAAQKPk9AA0fvx4FRUVKTExUfn5+QoKClJ6errtQue8vDy5uPzvQNWIESO0cuVKzZo1SzNnzlSfPn2UlpamgQMHOqsFAADQxDg9AElSbGysYmNjHS5bv359lbGoqChFRUXVePuOrvsBAADm5fQvQgQAAGhoBCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6BCAAAGA6tQpA3333XV3XAQAA0GBqFYB69+6ta6+9Vq+//rp++umnuq4JAACgXtUqAOXm5urKK69UXFycrFar7rnnHm3cuLGuawMAAKgXtQpAQUFBWrx4sQ4dOqQVK1bo8OHDGjlypAYOHKjk5GQVFRXVdZ0AAAB15pIugm7RooXGjRun1atXa8GCBdqzZ48efvhh+fv7a+LEiTp8+HBd1QkAAFBnLikAbdq0SX/605/UpUsXJScn6+GHH9bevXuVkZGhQ4cOaezYsXVVJwAAQJ1pUZuVkpOT9dJLL2nnzp266aab9Oqrr+qmm26Si8vPeeqyyy7Tyy+/rJ49e9ZlrQAAAHWiVgFo2bJl+uMf/6jo6Gh16dLF4ZzOnTvrxRdfvKTiAAAA6kOtAlBGRoa6d+9uO+JzjmEYOnDggLp37y43NzdNmjSpTooEAACoS7W6BqhXr14qLi6uMn706FFddtlll1wUAABAfapVADIMw+H4yZMn5eHhcUkFAQAA1LeLOgUWFxcnSbJYLEpMTFTr1q1tyyoqKrRhwwYFBQXVaYEAAAB17aIC0ObNmyX9fARo27ZtcnNzsy1zc3NTYGCgHn744bqtEAAAoI5dVABat26dJCkmJkaLFy+Wl5dXvRQFAABQn2p1F9hLL71U13UAAAA0mBoHoHHjxunll1+Wl5eXxo0bd965a9asueTCAAAA6kuNA5C3t7csFovt3wEAAJqqGgegX5724hQYAABoymr1PUCnT5/WqVOnbM/379+vlJQUffjhh3VWGAAAQH2pVQAaO3asXn31VUnSsWPHNHz4cC1cuFBjx47VsmXL6rRAAACAularAJSbm6v/+7//kyT985//lNVq1f79+/Xqq6/qmWeeqdMCAQAA6lqtAtCpU6fUtm1bSdKHH36ocePGycXFRVdffbX2799fpwUCAADUtVoFoN69eystLU0HDhzQBx98oBtuuEGSVFhYyJcjAgCARq9WASgxMVEPP/ywevbsqeDgYIWEhEj6+WjQVVddVacFAgAA1LVafRP0rbfeqpEjR+rw4cMKDAy0jV9//fW6+eab66w4AACA+lCrACRJVqtVVqvVbmz48OGXXBAAAEB9q1UAKi0t1fz585WZmanCwkJVVlbaLf/uu+/qpDgAAID6UKtrgO6++269+OKL+r//+z/FxsZq+vTpdo+LtXTpUvXs2VMeHh4KDg7Wxo0bzzt/9erVCggIkIeHhwYNGqS1a9faLZ8zZ44CAgLk6emp9u3bKywsTBs2bLjougAAQPNUqyNA77//vt577z395je/ueQC3nzzTcXFxSk1NVXBwcFKSUlReHi4du7cqc6dO1eZn5WVpQkTJigpKUm/+93vtHLlSkVGRio3N1cDBw6UJF1xxRVasmSJLr/8cp0+fVqLFi3SDTfcoD179qhTp06XXDMAAGjaanUEqH379urQoUOdFJCcnKwpU6YoJiZG/fv3V2pqqlq3bq0VK1Y4nL948WJFREQoPj5e/fr107x58zR48GAtWbLENueOO+5QWFiYLr/8cg0YMEDJyckqKSnR1q1b66RmAADQtNUqAM2bN0+JiYl2vwdWG+Xl5crJyVFYWNj/CnJxUVhYmLKzsx2uk52dbTdfksLDw6udX15eruXLl8vb29vujjUAAGBetToFtnDhQu3du1e+vr7q2bOnWrZsabc8Nze3RtspLi5WRUWFfH197cZ9fX21Y8cOh+vk5+c7nJ+fn2839u677+r222/XqVOn1KVLF2VkZMjHx8fhNsvKylRWVmZ7XlJSUqP6AQBA01SrABQZGVnHZdS9a6+9Vlu2bFFxcbGef/553XbbbdqwYYPD64qSkpI0d+5cJ1QJAACcoVYBaPbs2XXy4j4+PnJ1dVVBQYHdeEFBQZXvGDrHarXWaL6np6d69+6t3r176+qrr1afPn304osvKiEhoco2ExISFBcXZ3teUlIif3//2rYFAAAauVpdAyRJx44d0wsvvKCEhAQdPXpU0s+nvg4ePFjjbbi5uWnIkCHKzMy0jVVWViozM9P28xq/FhISYjdfkjIyMqqd/8vt/vI01y+5u7vLy8vL7gEAAJqvWh0B2rp1q8LCwuTt7a19+/ZpypQp6tChg9asWaO8vDy9+uqrNd5WXFycJk2apKFDh2r48OFKSUlRaWmpYmJiJEkTJ05U165dlZSUJEmaPn26QkNDtXDhQo0ePVqrVq3Spk2btHz5ckk/f0njX//6V40ZM0ZdunRRcXGxli5dqoMHDyoqKqo27QIAgGamVgEoLi5O0dHReuqpp9S2bVvb+E033aQ77rjjorY1fvx4FRUVKTExUfn5+QoKClJ6errtQue8vDy5uPzvQNWIESO0cuVKzZo1SzNnzlSfPn2UlpZm+w4gV1dX7dixQ6+88oqKi4vVsWNHDRs2TJ999pkGDBhQm3YBAEAzU6sA9OWXX+q5556rMt61a9cqd2PVRGxsrGJjYx0uW79+fZWxqKioao/meHh4aM2aNRddAwAAMI9aXQPk7u7u8FbxXbt28U3LAACg0atVABozZowef/xxnTlzRpJksViUl5enRx55RLfcckudFggAAFDXahWAFi5cqJMnT6pTp046ffq0QkND1bt3b7Vt21Z//etf67pGAACAOlWra4C8vb2VkZGh//73v/rqq6908uRJDR48uMpPVAAAADRGFx2AKisr9fLLL2vNmjXat2+fLBaLLrvsMlmtVhmGIYvFUh91AgAA1JmLOgVmGIbGjBmju+++WwcPHtSgQYM0YMAA7d+/X9HR0br55pvrq04AAIA6c1FHgF5++WV9+umnyszM1LXXXmu37OOPP1ZkZKReffVVTZw4sU6LBAAAqEsXdQToH//4h2bOnFkl/EjSddddp7/85S9644036qw4AACA+nBRAWjr1q2KiIiodvmNN96or7766pKLAgAAqE8XFYCOHj1q+4kKR3x9ffXjjz9eclEAAAD16aICUEVFhVq0qP6yIVdXV509e/aSiwIAAKhPF3URtGEYio6Olru7u8PlZWVldVIUAABAfbqoADRp0qQLzuEOMAAA0NhdVAB66aWX6qsOAACABlOr3wIDAABoyghAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdAhAAADAdBpFAFq6dKl69uwpDw8PBQcHa+PGjeedv3r1agUEBMjDw0ODBg3S2rVrbcvOnDmjRx55RIMGDZKnp6f8/Pw0ceJEHTp0qL7bAAAATYTTA9Cbb76puLg4zZ49W7m5uQoMDFR4eLgKCwsdzs/KytKECRM0efJkbd68WZGRkYqMjNT27dslSadOnVJubq4ee+wx5ebmas2aNdq5c6fGjBnTkG0BAIBGzOkBKDk5WVOmTFFMTIz69++v1NRUtW7dWitWrHA4f/HixYqIiFB8fLz69eunefPmafDgwVqyZIkkydvbWxkZGbrtttvUt29fXX311VqyZIlycnKUl5fXkK0BAIBGqoUzX7y8vFw5OTlKSEiwjbm4uCgsLEzZ2dkO18nOzlZcXJzdWHh4uNLS0qp9nePHj8tisahdu3YOl5eVlamsrMz2vKSkpOZN1EJRUVG9v4az7N+/X2fPnnV2GcB5lZ05o/379zu7jHpTXl4uNzc3Z5dRr5p7j829Py8vL3Xq1MmpNTg1ABUXF6uiokK+vr52476+vtqxY4fDdfLz8x3Oz8/Pdzj/p59+0iOPPKIJEybIy8vL4ZykpCTNnTu3Fh1cvKKiIt13xx0qO3KkQV6voZWWlangwAGVeXs7uxTAoSPl5fpu/37Nf+ABubu7O7ucOld25oy+P3RIvbt2VYsWTv0rvt409x6be3+S5N6xo5atXOnUENQ839n/78yZM7rttttkGIaWLVtW7byEhAS7o0olJSXy9/evl5pKSkpUduSIHnJ3l3+rVvXyGs70xY8/6q9nz6qCo0BopE5WVMjt7Fk96OamK6o5KtyUffHjj/rr6dOa5uraLPuTmn+Pzb2/A6dPa+GRIyopKTFvAPLx8ZGrq6sKCgrsxgsKCmS1Wh2uY7VaazT/XPjZv3+/Pv7442qP/kiSu7t7g/+foH+rVurl6dmgr9kQ9p8+7ewSgBrp5uHRrD+DzbU/qfn32Nz7kyT94rITZ3HqRdBubm4aMmSIMjMzbWOVlZXKzMxUSEiIw3VCQkLs5ktSRkaG3fxz4Wf37t366KOP1LFjx/ppAAAANElOPwUWFxenSZMmaejQoRo+fLhSUlJUWlqqmJgYSdLEiRPVtWtXJSUlSZKmT5+u0NBQLVy4UKNHj9aqVau0adMmLV++XNLP4efWW29Vbm6u3n33XVVUVNiuD+rQoUOzvqgMAADUjNMD0Pjx41VUVKTExETl5+crKChI6enptgud8/Ly5OLyvwNVI0aM0MqVKzVr1izNnDlTffr0UVpamgYOHChJOnjwoN555x1JUlBQkN1rrVu3Ttdcc02D9AUAABovpwcgSYqNjVVsbKzDZevXr68yFhUVpaioKIfze/bsKcMw6rI8AADQzDj9ixABAAAaGgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYDgEIAACYjtMD0NKlS9WzZ095eHgoODhYGzduPO/81atXKyAgQB4eHho0aJDWrl1rt3zNmjW64YYb1LFjR1ksFm3ZsqUeqwcAAE2RUwPQm2++qbi4OM2ePVu5ubkKDAxUeHi4CgsLHc7PysrShAkTNHnyZG3evFmRkZGKjIzU9u3bbXNKS0s1cuRILViwoKHaAAAATYxTA1BycrKmTJmimJgY9e/fX6mpqWrdurVWrFjhcP7ixYsVERGh+Ph49evXT/PmzdPgwYO1ZMkS25y77rpLiYmJCgsLa6g2AABAE+O0AFReXq6cnBy7oOLi4qKwsDBlZ2c7XCc7O7tKsAkPD692fk2VlZWppKTE7gEAAJovpwWg4uJiVVRUyNfX127c19dX+fn5DtfJz8+/qPk1lZSUJG9vb9vD39//krYHAAAaN6dfBN0YJCQk6Pjx47bHgQMHnF0SAACoRy2c9cI+Pj5ydXVVQUGB3XhBQYGsVqvDdaxW60XNryl3d3e5u7tf0jYAAEDT4bQjQG5ubhoyZIgyMzNtY5WVlcrMzFRISIjDdUJCQuzmS1JGRka18wEAABxx2hEgSYqLi9OkSZM0dOhQDR8+XCkpKSotLVVMTIwkaeLEieratauSkpIkSdOnT1doaKgWLlyo0aNHa9WqVdq0aZOWL19u2+bRo0eVl5enQ4cOSZJ27twp6eejR5d6pAgAADQPTg1A48ePV1FRkRITE5Wfn6+goCClp6fbLnTOy8uTi8v/DlKNGDFCK1eu1KxZszRz5kz16dNHaWlpGjhwoG3OO++8YwtQknT77bdLkmbPnq05c+Y0TGMAAKBRc2oAkqTY2FjFxsY6XLZ+/foqY1FRUYqKiqp2e9HR0YqOjq6j6gAAQHPEXWAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0CEAAAMB0GkUAWrp0qXr27CkPDw8FBwdr48aN552/evVqBQQEyMPDQ4MGDdLatWvtlhuGocTERHXp0kWtWrVSWFiYdu/eXZ8tAACAJsTpAejNN99UXFycZs+erdzcXAUGBio8PFyFhYUO52dlZWnChAmaPHmyNm/erMjISEVGRmr79u22OU899ZSeeeYZpaamasOGDfL09FR4eLh++umnhmoLAAA0Yk4PQMnJyZoyZYpiYmLUv39/paamqnXr1lqxYoXD+YsXL1ZERITi4+PVr18/zZs3T4MHD9aSJUsk/Xz0JyUlRbNmzdLYsWN15ZVX6tVXX9WhQ4eUlpbWgJ0BAIDGyqkBqLy8XDk5OQoLC7ONubi4KCwsTNnZ2Q7Xyc7OtpsvSeHh4bb533//vfLz8+3meHt7Kzg4uNptAgAAc2nhzBcvLi5WRUWFfH197cZ9fX21Y8cOh+vk5+c7nJ+fn29bfm6sujm/VlZWprKyMtvz48ePS5JKSkouopuaOXHihM5UVGjHiRM6cfZsnW/f2faWlqrCMLSrtFQVLVs6u5w6d/D0aZ0qK9M333yjEydOOLucenHgwAH9VFbGn9Emqrn3JzX/Hpt7fwdPn9aZigqdOHGizv87e257hmFccK5TA1BjkZSUpLlz51YZ9/f3r7fX/KDettw43Lptm7NLqFcfjxnj7BLq3UfOLqCeNfc/o829P6n599jc+/vgqqvqbdsnTpyQt7f3eec4NQD5+PjI1dVVBQUFduMFBQWyWq0O17Fareedf+6fBQUF6tKli92coKAgh9tMSEhQXFyc7XllZaWOHj2qjh07ymKxXHRf51NSUiJ/f38dOHBAXl5edbrtxoD+mr7m3iP9NX3NvUf6qz3DMHTixAn5+fldcK5TA5Cbm5uGDBmizMxMRUZGSvo5fGRmZio2NtbhOiEhIcrMzNSMGTNsYxkZGQoJCZEkXXbZZbJarcrMzLQFnpKSEm3YsEH33Xefw226u7vL3d3dbqxdu3aX1NuFeHl5Ncs/2OfQX9PX3Hukv6avufdIf7VzoSM/5zj9FFhcXJwmTZqkoUOHavjw4UpJSVFpaaliYmIkSRMnTlTXrl2VlJQkSZo+fbpCQ0O1cOFCjR49WqtWrdKmTZu0fPlySZLFYtGMGTP0xBNPqE+fPrrsssv02GOPyc/PzxayAACAuTk9AI0fP15FRUVKTExUfn6+goKClJ6ebruIOS8vTy4u/7tZbcSIEVq5cqVmzZqlmTNnqk+fPkpLS9PAgQNtc/785z+rtLRUU6dO1bFjxzRy5Eilp6fLw8OjwfsDAACNj9MDkCTFxsZWe8pr/fr1VcaioqIUFRVV7fYsFosef/xxPf7443VVYp1xd3fX7Nmzq5xyay7or+lr7j3SX9PX3Hukv4ZhMWpyrxgAAEAz4vRvggYAAGhoBCAAAGA6BCAAAGA6BCAAAGA6BKA68Omnn+r3v/+9/Pz8ZLFYHP7q/LfffqsxY8bI29tbnp6eGjZsmPLy8mzLf/rpJ91///3q2LGj2rRpo1tuuaXKN147S130d80118hisdg97r333gbs4vwu1OOvaz/3ePrpp21zjh49qjvvvFNeXl5q166dJk+erJMnTzZwJ47VRX89e/assnz+/PkN3IljF+rv5MmTio2NVbdu3dSqVSv1799fqampdnMa82dQqpseG/Pn8EL9FRQUKDo6Wn5+fmrdurUiIiK0e/duuzmNeR/WRX+Nef8lJSVp2LBhatu2rTp37qzIyEjt3LnTbk5N9k9eXp5Gjx6t1q1bq3PnzoqPj9fZevpNQgJQHSgtLVVgYKCWLl3qcPnevXs1cuRIBQQEaP369dq6dasee+wxu+8levDBB/Wf//xHq1ev1ieffKJDhw5p3LhxDdXCedVFf5I0ZcoUHT582PZ46qmnGqL8GrlQj7+s+/Dhw1qxYoUsFotuueUW25w777xTX3/9tTIyMvTuu+/q008/1dSpUxuqhfOqi/4k6fHHH7eb98ADDzRE+Rd0of7i4uKUnp6u119/Xd9++61mzJih2NhYvfPOO7Y5jfkzKNVNj1Lj/Ryerz/DMBQZGanvvvtOb7/9tjZv3qwePXooLCxMpaWltnmNeR/WRX9S491/n3zyie6//3598cUXysjI0JkzZ3TDDTdc1P6pqKjQ6NGjVV5erqysLL3yyit6+eWXlZiYWD9FG6hTkox///vfdmPjx483/vCHP1S7zrFjx4yWLVsaq1evto19++23hiQjOzu7vkqtldr0ZxiGERoaakyfPr3+CqtDjnr8tbFjxxrXXXed7fk333xjSDK+/PJL29j7779vWCwW4+DBg/VVaq3Upj/DMIwePXoYixYtqr/C6oij/gYMGGA8/vjjdmODBw82Hn30UcMwmtZn0DBq16NhNJ3P4a/727lzpyHJ2L59u22soqLC6NSpk/H8888bhtG09mFt+jOMprP/DMMwCgsLDUnGJ598YhhGzfbP2rVrDRcXFyM/P982Z9myZYaXl5dRVlZW5zVyBKieVVZW6r333tMVV1yh8PBwde7cWcHBwXaHP3NycnTmzBmFhYXZxgICAtS9e3dlZ2c7oeqaq0l/57zxxhvy8fHRwIEDlZCQoFOnTjV8wXWgoKBA7733niZPnmwby87OVrt27TR06FDbWFhYmFxcXLRhwwZnlFlrjvo7Z/78+erYsaOuuuoqPf300/V2aLqujRgxQu+8844OHjwowzC0bt067dq1SzfccIOkpv0ZPOdCPZ7TFD+HZWVlkmR3VNnFxUXu7u76/PPPJTXtfViT/s5pKvvv+PHjkqQOHTpIqtn+yc7O1qBBg2y/BCFJ4eHhKikp0ddff13nNTaKb4JuzgoLC3Xy5EnNnz9fTzzxhBYsWKD09HSNGzdO69atU2hoqPLz8+Xm5lblB1h9fX2Vn5/vnMJrqCb9SdIdd9yhHj16yM/PT1u3btUjjzyinTt3as2aNU7u4OK98soratu2rd2h2/z8fHXu3NluXosWLdShQ4dGvw9/zVF/kjRt2jQNHjxYHTp0UFZWlhISEnT48GElJyc7qdKae/bZZzV16lR169ZNLVq0kIuLi55//nmNGjVKkpr0Z/CcC/UoNd3P4bn/UCYkJOi5556Tp6enFi1apB9++EGHDx+W1LT3YU36k5rO/qusrNSMGTP0m9/8xvYzVTXZP/n5+Xbh59zyc8vqGgGonlVWVkqSxo4dqwcffFCSFBQUpKysLKWmptoCQlNV0/5+eS3MoEGD1KVLF11//fXau3evevXq1fCFX4IVK1bozjvvbLa/LVddf3FxcbZ/v/LKK+Xm5qZ77rlHSUlJTv9K+wt59tln9cUXX+idd95Rjx499Omnn+r++++Xn5+f3f+RNmU16bGpfg5btmypNWvWaPLkyerQoYNcXV0VFhamG2+8UUYz+DGDmvbXVPbf/fffr+3bt1c5etXYcAqsnvn4+KhFixbq37+/3Xi/fv1sd0lZrVaVl5fr2LFjdnMKCgpktVobqtRaqUl/jgQHB0uS9uzZU6/11bXPPvtMO3fu1N133203brVaVVhYaDd29uxZHT16tNHvw1+qrj9HgoODdfbsWe3bt6/+C7sEp0+f1syZM5WcnKzf//73uvLKKxUbG6vx48frb3/7m6Sm/RmUatajI03pczhkyBBt2bJFx44d0+HDh5Wenq4jR47o8ssvl9T09+GF+nOkMe6/2NhYvfvuu1q3bp26detmG6/J/rFarVXuCjv3vD72IQGonrm5uWnYsGFVbgfctWuXevToIennP/gtW7ZUZmambfnOnTuVl5enkJCQBq33YtWkP0e2bNkiSerSpUt9llfnXnzxRQ0ZMkSBgYF24yEhITp27JhycnJsYx9//LEqKyttf0k1BdX158iWLVvk4uJS5dRfY3PmzBmdOXNGLi72f925urrajmA25c+gVLMeHWmKn0Nvb2916tRJu3fv1qZNmzR27FhJTX8fnlNdf440pv1nGIZiY2P173//Wx9//LEuu+wyu+U12T8hISHatm2b3f9MZmRkyMvLq8r/ZNdV0bhEJ06cMDZv3mxs3rzZkGQkJycbmzdvNvbv328YhmGsWbPGaNmypbF8+XJj9+7dxrPPPmu4uroan332mW0b9957r9G9e3fj448/NjZt2mSEhIQYISEhzmrJzqX2t2fPHuPxxx83Nm3aZHz//ffG22+/bVx++eXGqFGjnNmWnQv1aBiGcfz4caN169bGsmXLHG4jIiLCuOqqq4wNGzYYn3/+udGnTx9jwoQJDdXCeV1qf1lZWcaiRYuMLVu2GHv37jVef/11o1OnTsbEiRMbso1qXai/0NBQY8CAAca6deuM7777znjppZcMDw8P4+9//7ttG435M2gYl95jY/8cXqi/t956y1i3bp2xd+9eIy0tzejRo4cxbtw4u2005n14qf019v133333Gd7e3sb69euNw4cP2x6nTp2yzbnQ/jl79qwxcOBA44YbbjC2bNlipKenG506dTISEhLqpWYCUB1Yt26dIanKY9KkSbY5L774otG7d2/Dw8PDCAwMNNLS0uy2cfr0aeNPf/qT0b59e6N169bGzTffbBw+fLiBO3HsUvvLy8szRo0aZXTo0MFwd3c3evfubcTHxxvHjx93QjeO1aTH5557zmjVqpVx7Ngxh9s4cuSIMWHCBKNNmzaGl5eXERMTY5w4caKBOji/S+0vJyfHCA4ONry9vQ0PDw+jX79+xpNPPmn89NNPDdhF9S7U3+HDh43o6GjDz8/P8PDwMPr27WssXLjQqKystG2jMX8GDePSe2zsn8ML9bd48WKjW7duRsuWLY3u3bsbs2bNqnJrdGPeh5faX2Pff456k2S89NJLtjk12T/79u0zbrzxRqNVq1aGj4+P8dBDDxlnzpypl5ot/79wAAAA0+AaIAAAYDoEIAAAYDoEIAAAYDoEIAAAYDoEIAAAYDoEIAAAYDoEIAAAYDoEIAAAYDoEIAAAYDoEIAAAYDoEIADNXlFRkaxWq5588knbWFZWltzc3Ox+nRqAefBbYABMYe3atYqMjFRWVpb69u2roKAgjR07VsnJyc4uDYATEIAAmMb999+vjz76SEOHDtW2bdv05Zdfyt3d3dllAXACAhAA0zh9+rQGDhyoAwcOKCcnR4MGDXJ2SQCchGuAAJjG3r17dejQIVVWVmrfvn3OLgeAE3EECIAplJeXa/jw4QoKClLfvn2VkpKibdu2qXPnzs4uDYATEIAAmEJ8fLz++c9/6quvvlKbNm0UGhoqb29vvfvuu84uDYATcAoMQLO3fv16paSk6LXXXpOXl5dcXFz02muv6bPPPtOyZcucXR4AJ+AIEAAAMB2OAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANMhAAEAANP5f8JzFVDT37TkAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# specifying bin-edges:\n",
    "plt.hist(x, bins=[160,165,170,175,180,185,190,195,200], edgecolor='black', color='red', alpha=0.7, density=True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Density')\n",
    "plt.title('Histogram Example')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Histograms are important - they show how the data is **distributed** <br>\n",
    "\n",
    "Next week we will talk more about theoretical distributions. <br>\n",
    "\n",
    "Histograms serve as *empirical distributions* <br>\n",
    "\n",
    "Based on the histogram above, how would you guess the height-distribution in the *population* looks like? <br> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets try with really small bins, such that the histogram diplays all the details in the data:\n",
    "plt.hist(x, bins=np.arange(160,200,1), edgecolor='black', color='red', alpha=0.7, density=True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Density')\n",
    "plt.title('Histogram Example')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cumulative distribution\n",
    "\n",
    "The \"detailed\" histogram with small bins is maybe not the nicest way to display data. <br>\n",
    "\n",
    "But histograms are dependent on bin-choices, which is also (sometimes) not ideal.. <br>\n",
    "\n",
    "An alternative is to do a cumulative kind of plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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N089+9jO9++67qqqq0oYNG9p9jIaGBjU0NPjv19TUyOVyqbq6WrGxscFMF93MsizdWlCski++ND0V9FCfLs5SjCPofwcBCEE1NTWKi4vr8PU7qMs0jY2NKikpkcfj+d8PiIiQx+NRcXFxu/stXrxYgwYN0syZMwN6nPz8fMXFxflvLpcrmGnCoPqmZkIE7cpIiVd0pN30NAD0MEH98+T48eNqbm5WYmJii/HExETt2bOnzX3ee+89rVmzRqWlpQE/Tk5Ojrxer//+N2dGEFp2LfQoxsELD/4nOtIum81mehoAepguPVd68uRJ3XnnnVq9erUSEhIC3s/pdMrpdHbhzNAdYhx2TscDADoU1CtFQkKC7Ha7KisrW4xXVlYqKSmp1fb79+/XwYMHNWnSJP+Yz+f7+oH79FFZWZkuuOCCs5k3AAAIE0G9Z8ThcCg9PV1FRUX+MZ/Pp6KiImVmZrbafvjw4fr4449VWlrqv914442aOHGiSktLufQCAACCv0zj9Xo1ffp0ZWRkaOzYsVqxYoVqa2s1Y8YMSVJ2draGDBmi/Px8RUVF6dJLL22xf79+/SSp1TgAAOidgo6RKVOm6NixY8rNzVVFRYVGjRqlwsJC/5tay8vLFRHBB7sCAIDABP05IyYE+nvKMK+u8bQuyX1bEp8nAQC9XZd8zggAAEBnI0YAAIBRxAgAADCKGAEAAEYRIwAAwChiBAAAGEWMAAAAo4gRAABgFDECAACMIkYAAIBRxAgAADCKGAEAAEYRIwAAwChiBAAAGEWMAAAAo4gRAABgFDECAACMIkYAAIBRxAgAADCKGAEAAEYRIwAAwChiBAAAGEWMAAAAo4gRAABgFDECAACMIkYAAIBRxAgAADCqj+kJoGezLEv1Tc0Bb1/XGPi2AABIxAjOwLIs3VpQrJIvvjQ9FQBAGOMyDdpV39R81iGSkRKv6Eh7J88IABCOODOCgOxa6FGMI/C4iI60y2azdeGMAADhghhBQGIcdsU4+OsCAOh8XKYBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUWcVI6tWrVJqaqqioqLkdru1c+fOdrddvXq1rrnmGsXHxys+Pl4ej+eM2wMAgN4l6BhZt26dvF6v8vLy9MEHHygtLU1ZWVk6evRom9tv27ZNU6dO1datW1VcXCyXy6Vrr71Whw8fPufJI3iWZamu8XSAt2bT0wUA9AI2y7KsYHZwu90aM2aMVq5cKUny+XxyuVyaM2eOFixY0OH+zc3Nio+P18qVK5Wdnd3mNg0NDWpoaPDfr6mpkcvlUnV1tWJjY4OZLr7FsizdWlCski++DHrfTxdnKcbRpwtmBQAIVzU1NYqLi+vw9TuoMyONjY0qKSmRx+P53w+IiJDH41FxcXFAP6Ourk5NTU3q379/u9vk5+crLi7Of3O5XMFME+2ob2o+qxDJSIlXdKS9C2YEAIAU1D91jx8/rubmZiUmJrYYT0xM1J49ewL6GfPnz1dycnKLoPmunJwceb1e//1vzoyg8+xa6FGMI7DAiI60y2azdfGMAAC9Vbeed1+yZIleeeUVbdu2TVFRUe1u53Q65XQ6u3FmvU+Mw85lFwBAjxDUq1FCQoLsdrsqKytbjFdWViopKemM+z711FNasmSJ/va3v2nkyJHBzxQAAISloN4z4nA4lJ6erqKiIv+Yz+dTUVGRMjMz293vySef1KOPPqrCwkJlZGSc/WwBAEDYCfo8vdfr1fTp05WRkaGxY8dqxYoVqq2t1YwZMyRJ2dnZGjJkiPLz8yVJTzzxhHJzc/Xyyy8rNTVVFRUVkqS+ffuqb9++nbgUAAAQioKOkSlTpujYsWPKzc1VRUWFRo0apcLCQv+bWsvLyxUR8b8TLn/4wx/U2NioW2+9tcXPycvL029+85tzmz0AAAh5QX/OiAmB/p4yzqyu8bQuyX1bEp8bAgDoel3yOSMAAACdjRgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMCoPqYnYJJlWapvajY9jW5T19h71goACB29NkYsy9KtBcUq+eJL01MBAKBX67WXaeqbmnttiGSkxCs60m56GgAASOrFZ0a+bddCj2IcvefFOTrSLpvNZnoaAABIIkYkSTEOu2Ic/F8BAIAJvfYyDQAA6BmIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMAoYgQAABhFjAAAAKOIEQAAYBQxAgAAjCJGAACAUcQIAAAwihgBAABGESMAAMCos4qRVatWKTU1VVFRUXK73dq5c+cZt1+/fr2GDx+uqKgoXXbZZdq8efNZTRYAAISfoGNk3bp18nq9ysvL0wcffKC0tDRlZWXp6NGjbW6/Y8cOTZ06VTNnztSHH36oyZMna/Lkyfrkk0/OefIAACD02SzLsoLZwe12a8yYMVq5cqUkyefzyeVyac6cOVqwYEGr7adMmaLa2lq99dZb/rErrrhCo0aNUkFBQZuP0dDQoIaGBv/96upqDRs2TIcOHVJsbGww021XXeNpjf1tkSRp58M/UoyjT6f8XAAA8LWamhq5XC5VVVUpLi6u/Q2tIDQ0NFh2u916/fXXW4xnZ2dbN954Y5v7uFwu6+mnn24xlpuba40cObLdx8nLy7MkcePGjRs3btzC4Hbo0KEz9kVQpwOOHz+u5uZmJSYmthhPTEzUnj172tynoqKize0rKirafZycnBx5vV7/fZ/PpxMnTmjAgAGy2Wzt7vdNgXXmGZSejjWz5nDFmllzuOpNa7YsSydPnlRycvIZt+uR1yacTqecTmeLsX79+gW8f2xsbNgf4O9izb0Da+4dWHPv0FvWfMbLM/8vqDewJiQkyG63q7KyssV4ZWWlkpKS2twnKSkpqO0BAEDvElSMOBwOpaenq6ioyD/m8/lUVFSkzMzMNvfJzMxssb0kbdmypd3tAQBA7xL0ZRqv16vp06crIyNDY8eO1YoVK1RbW6sZM2ZIkrKzszVkyBDl5+dLkubOnavx48dr2bJluuGGG/TKK69o165dev755zt3Jfr68k5eXl6rSzzhjDX3Dqy5d2DNvUNvXHNHgv7VXklauXKlli5dqoqKCo0aNUq///3v5Xa7JUkTJkxQamqqXnjhBf/269ev18KFC3Xw4EF9//vf15NPPqnrr7++0xYBAABC11nFCAAAQGfhu2kAAIBRxAgAADCKGAEAAEYRIwAAwKgeHyPbt2/XpEmTlJycLJvNpg0bNrTaZvfu3brxxhsVFxen8847T2PGjFF5ebn/z7/66ivNnj1bAwYMUN++fXXLLbe0+iC2nqQz1jxhwgTZbLYWt3vvvbcbVxGcjtb83bV8c1u6dKl/mxMnTuj2229XbGys+vXrp5kzZ+rUqVPdvJLAdcaaU1NTW/35kiVLunklgetozadOndL999+voUOHKjo6WpdcckmrL9QMt+dzIGsOt+dzZWWl7rrrLiUnJysmJkbXXXedPvvssxbbhNtxDmTNoXacO1OPj5Ha2lqlpaVp1apVbf75/v37dfXVV2v48OHatm2bPvroIy1atEhRUVH+bebNm6c333xT69ev1zvvvKP//Oc/uvnmm7trCUHrjDVL0qxZs3TkyBH/7cknn+yO6Z+Vjtb87XUcOXJEa9eulc1m0y233OLf5vbbb9e//vUvbdmyRW+99Za2b9+ue+65p7uWELTOWLMkLV68uMV2c+bM6Y7pn5WO1uz1elVYWKiXXnpJu3fv1gMPPKD7779fGzdu9G8Tbs/nQNYshc/z2bIsTZ48WQcOHNAbb7yhDz/8UCkpKfJ4PKqtrfVvF07HOdA1S6F1nDvVmb+nt2eR1Oobg6dMmWLdcccd7e5TVVVlRUZGWuvXr/eP7d6925JkFRcXd9VUO83ZrNmyLGv8+PHW3Llzu25iXaitNX/XTTfdZP3whz/03//0008tSdY///lP/9hf//pXy2azWYcPH+6qqXaas1mzZVlWSkpKq2/FDhVtrfkHP/iBtXjx4hZjl19+ufXwww9blhWez+eO1mxZ4fV8LisrsyRZn3zyiX+subnZGjhwoLV69WrLssLvOAeyZssK7eN8rnr8mZEz8fl82rRpky666CJlZWVp0KBBcrvdLU6PlZSUqKmpSR6Pxz82fPhwDRs2TMXFxQZmfW4CWfM3/vznPyshIUGXXnqpcnJyVFdX1/0T7gKVlZXatGmTZs6c6R8rLi5Wv379lJGR4R/zeDyKiIjQ+++/b2KanaqtNX9jyZIlGjBggEaPHq2lS5fq9OnTBmbYOa688kpt3LhRhw8flmVZ2rp1q/bu3atrr71WUvg9n6WO1/yNcHk+NzQ0SFKLM7kRERFyOp167733JIXfcQ5kzd8Il+McrB75rb2BOnr0qE6dOqUlS5boscce0xNPPKHCwkLdfPPN2rp1q8aPH6+Kigo5HI5W3/qbmJioiooKMxM/B4GsWZKmTZumlJQUJScn66OPPtL8+fNVVlam1157zfAKzt2LL76o888/v8Up24qKCg0aNKjFdn369FH//v1D8jh/V1trlqRf/vKXuvzyy9W/f3/t2LFDOTk5OnLkiJYvX25opufmmWee0T333KOhQ4eqT58+ioiI0OrVqzVu3DhJCrvns9TxmqXwej5/ExU5OTl67rnndN555+npp5/Wv//9bx05ckRS+B3nQNYshddxDlZIx4jP55Mk3XTTTZo3b54kadSoUdqxY4cKCgr8L8zhJNA1f/u9EpdddpkGDx6sH/3oR9q/f78uuOCC7p94J1q7dq1uv/32Vu+RCWftrdnr9fr/98iRI+VwOPTzn/9c+fn5Ifm9F88884z+8Y9/aOPGjUpJSdH27ds1e/ZsJScnt/hXcjgJZM3h9HyOjIzUa6+9ppkzZ6p///6y2+3yeDz6yU9+IitMPxA80DWH03EOVkjHSEJCgvr06aNLLrmkxfiIESP8p76SkpLU2NioqqqqFpVdWVmppKSk7pxupwhkzW355ruD9u3bF9J/qd99912VlZVp3bp1LcaTkpJ09OjRFmOnT5/WiRMnQvI4f1t7a26L2+3W6dOndfDgQV188cXdMLvOU19fr4ceekivv/66brjhBklfB1ZpaameeuopeTyesHs+B7LmtoT68zk9PV2lpaWqrq5WY2OjBg4cKLfb7b/MGm7HWep4zW0J9eMcjJB+z4jD4dCYMWNUVlbWYnzv3r1KSUmR9PVfgMjISBUVFfn/vKysTOXl5crMzOzW+XaGQNbcltLSUknS4MGDu3J6XW7NmjVKT09XWlpai/HMzExVVVWppKTEP/b3v/9dPp/P/4QOVe2tuS2lpaWKiIhodckqFDQ1NampqUkRES3/s2S32/1nBMPt+RzImtsSLs/nuLg4DRw4UJ999pl27dqlm266SVL4Hedva2/NbQmX4xyIHn9m5NSpU9q3b5///ueff67S0lL1799fw4YN04MPPqgpU6Zo3LhxmjhxogoLC/Xmm29q27Ztkr4+8DNnzpTX61X//v0VGxurOXPmKDMzU1dccYWhVZ3Zua55//79evnll3X99ddrwIAB+uijjzRv3jyNGzdOI0eONLSqM+tozZJUU1Oj9evXa9myZa32HzFihK677jrNmjVLBQUFampq0v3336/bbrtNycnJ3baOYJzrmouLi/X+++9r4sSJOv/881VcXKx58+bpjjvuUHx8fLetIxgdrXn8+PF68MEHFR0drZSUFL3zzjv605/+5H8PTDg+nztaczg+n9evX6+BAwdq2LBh+vjjjzV37lxNnjzZ/6bdcDzOHa05FI9zpzL7yzwd27p1qyWp1W369On+bdasWWNdeOGFVlRUlJWWlmZt2LChxc+or6+3fvGLX1jx8fFWTEyM9dOf/tQ6cuRIN68kcOe65vLycmvcuHFW//79LafTaV144YXWgw8+aFVXVxtYTWACWfNzzz1nRUdHW1VVVW3+jP/+97/W1KlTrb59+1qxsbHWjBkzrJMnT3bTCoJ3rmsuKSmx3G63FRcXZ0VFRVkjRoywHn/8ceurr77qxlUEp6M1HzlyxLrrrrus5ORkKyoqyrr44outZcuWWT6fz/8zwu353NGaw/H5/Lvf/c4aOnSoFRkZaQ0bNsxauHCh1dDQ0OJnhNtx7mjNoXicO5PNssL0HUMAACAkhPR7RgAAQOgjRgAAgFHECAAAMIoYAQAARhEjAADAKGIEAAAYRYwAAACjiBEAAGAUMQIAAIwiRgAAgFHECAAAMOr/ACALanBT6zk7AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the \"empirical cumulated density function\"\n",
    "plt.ecdf(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[161 166 167 168 179 179 184 187 191 198]\n"
     ]
    }
   ],
   "source": [
    "# compare with values \n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the cumulated distribution all detailed information is kept - but is is another way to visualise the distribution of data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets increase the y-range slightly:\n",
    "plt.ecdf(x)\n",
    "plt.ylim(-0.1,1.1)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('ecdf(x)')\n",
    "plt.title('Epirical cumulated density function')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The y-range goes from 0 to 1 - or 0% to 100% <br>\n",
    "\n",
    "Every vertical line-segment is a datapoint <br>\n",
    "\n",
    "When the plot is \"steep\" there are many datapoints (corresponds to high values in the histogram). <br>\n",
    "\n",
    "The cumulated plot can be used to understand the \"averaged_inverted_cdf\" used for percentiles. <br>\n",
    "\n",
    "OBS: we will talk more about distributions - and cumulative distributions - over the next couple of weeks. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other plots in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make a boxplot\n",
    "plt.boxplot(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the *values* are on the **y-axis**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Adding some explanation:\n",
    "plt.boxplot(x)\n",
    "plt.text(1.1, np.percentile(x,  [0]), 'Minimum', color='blue')\n",
    "plt.text(1.1, np.percentile(x, [25]), 'Q1', color='blue')\n",
    "plt.text(1.1, np.percentile(x, [50]), 'Median', color='blue')\n",
    "plt.text(1.1, np.percentile(x, [75]), 'Q3', color='blue')\n",
    "plt.text(1.1, np.percentile(x,[100]), 'Maximun', color='blue')\n",
    "plt.title(\"Basic box plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "see documentation for definition of box and whiskers: \n",
    "\n",
    "https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.boxplot.html#matplotlib.axes.Axes.boxplot\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Adding an outlier to the data:\n",
    "plt.boxplot(np.append(x, [235]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8,4))\n",
    "ax1.boxplot(np.append(x, [235]))\n",
    "ax2.boxplot(np.append(x, [235]), whis=(0,100))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working with data - dataframes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the Pandas library\n",
    "import pandas as pd "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "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>males</th>\n",
       "      <th>females</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>152</td>\n",
       "      <td>159.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>171</td>\n",
       "      <td>166.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>173</td>\n",
       "      <td>168.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>173</td>\n",
       "      <td>168.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>178</td>\n",
       "      <td>171.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>179</td>\n",
       "      <td>171.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>180</td>\n",
       "      <td>172.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>180</td>\n",
       "      <td>172.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>182</td>\n",
       "      <td>173.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>182</td>\n",
       "      <td>174.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>182</td>\n",
       "      <td>175.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>185</td>\n",
       "      <td>175.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>185</td>\n",
       "      <td>175.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>185</td>\n",
       "      <td>175.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>185</td>\n",
       "      <td>175.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>185</td>\n",
       "      <td>177.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>186</td>\n",
       "      <td>178.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>187</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>190</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>190</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>192</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>192</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>197</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    males  females\n",
       "0     152    159.0\n",
       "1     171    166.0\n",
       "2     173    168.0\n",
       "3     173    168.0\n",
       "4     178    171.0\n",
       "5     179    171.0\n",
       "6     180    172.0\n",
       "7     180    172.0\n",
       "8     182    173.0\n",
       "9     182    174.0\n",
       "10    182    175.0\n",
       "11    185    175.0\n",
       "12    185    175.0\n",
       "13    185    175.0\n",
       "14    185    175.0\n",
       "15    185    177.0\n",
       "16    186    178.0\n",
       "17    187      NaN\n",
       "18    190      NaN\n",
       "19    190      NaN\n",
       "20    192      NaN\n",
       "21    192      NaN\n",
       "22    197      NaN"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make a DataFrame:\n",
    "data = pd.DataFrame({\n",
    "    'males':  [152, 171, 173, 173, 178, 179, 180, 180, 182, 182, 182, 185, \n",
    "                    185 ,185, 185, 185 ,186 ,187 ,190 ,190, 192, 192, 197], \n",
    "    'females':[159, 166, 168 ,168 ,171 ,171 ,172, 172, 173, 174 ,175 ,175,\n",
    "                    175, 175, 175, 177, 178, np.nan,np.nan,np.nan,np.nan,np.nan,np.nan]\n",
    "})\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n"
     ]
    }
   ],
   "source": [
    "print(type(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The DataFrame has a direct method for making a boxplot:\n",
    "data.boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reading data from an external file\n",
    "\n",
    "It is very important to learn how to read data from other files. In practice one will never type all the data into Python by hand!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "csv_data= pd.read_csv(\"studentheights.csv\", sep=';')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n"
     ]
    }
   ],
   "source": [
    "print(type(csv_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "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>Height</th>\n",
       "      <th>Gender</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>152</td>\n",
       "      <td>male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>171</td>\n",
       "      <td>male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>173</td>\n",
       "      <td>male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>173</td>\n",
       "      <td>male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>178</td>\n",
       "      <td>male</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Height Gender\n",
       "0     152   male\n",
       "1     171   male\n",
       "2     173   male\n",
       "3     173   male\n",
       "4     178   male"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "csv_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that this DataFrame is differently structured compared to the one from above (which had columns: \"males\" and \"females\").\n",
    "\n",
    "If we wnt to do a boxplot by gender, we need to include the \"by=..\" argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Height'}, xlabel='[Gender]'>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "csv_data.boxplot(by='Gender')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See the book for more plots (scatterplots, pie charts etc.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pernille",
   "language": "python",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}