{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "A6iFUUQLNDlE"
   },
   "source": [
    "<table class=\"m01-notebook-buttons\" align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/yy/dviz-course/blob/master/docs/m10-logscale/lab10.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a href=\"https://yyahn.com/dviz-course/m10-logscale/lab10/\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View on Github</a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a href=\"https://raw.githubusercontent.com/yy/dviz-course/master/docs/m10-logscale/lab10.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View raw on Github</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sylchE7jCpQP"
   },
   "source": [
    "# Module 10: Logscale\n",
    "\n",
    "In this module, we will learn why we want to use log scale for some types of data and strategies for using log scale. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "9xAAtok8CpQS",
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import vega_datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XPs_sZrtCpQT"
   },
   "source": [
    "## Ratio and logarithm\n",
    "\n",
    "If you use linear scale to visualize ratios, it can be quite misleading. As learned in the class, ratio values larger than 1 can vary between 1 and infinite, while ratio values smaller than 1 can vary only between 0 and 1. For instance, the ratios of 100:1 (100/1) or 1000:1 (1000/1) are represented as 100 and 1000. The corresponding distances from 1:1 (1) are 99 and 999, respectively. On the other hand, the ratios of 1:100 (1/100) or 1:1000 (1/1000) are represented as 0.01 and 0.001. The corresponding distances from 1:1 (1) are 0.99 and 0.999, respectively. In other words, there is no symmetry between symmetric ratios! \n",
    "\n",
    "You can watch my video [Why you should use logarithmic scale when visualizing ratios](https://www.youtube.com/watch?v=Q9azoaH7gds). \n",
    "\n",
    "To see this clearly, let's first create some ratios."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "02uwOpjPCpQT",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "400ffda2-d774-4e8e-d544-5454d8fd3426"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.e-03 1.e-02 1.e-01 1.e+00 1.e+01 1.e+02 1.e+03]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1,    1,   1,  1, 10, 100, 1000])\n",
    "y = np.array([1000, 100, 10, 1, 1,  1,   1   ])\n",
    "ratio = x/y\n",
    "print(ratio)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZOV3oQV3CpQU"
   },
   "source": [
    "**Q: Plot on the linear scale using the [`scatter()`](http://matplotlib.org/examples/shapes_and_collections/scatter_demo.html) function. Also draw a horizontal line at ratio=1 for a reference. The x-axis will be simply the data ID that refers to each ratio data point. Y-axis will be the ratio values.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "lsamHuF0CpQU",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "6ca653d8-a7da-415f-919d-2cc40052959d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Ratio')"
      ]
     },
     "execution_count": 3,
     "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": [
    "X = np.arange(len(ratio))\n",
    "\n",
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tiPVu02nCpQV"
   },
   "source": [
    "**Q: Is this a good visualization of the ratio data? Why? Why not? Explain.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "33JTlQ07CpQV"
   },
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wOC-1c-WCpQW"
   },
   "source": [
    "**Q: Can you fix it?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "gCKaobcWCpQW",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "852092fc-1a3f-42ae-e77d-712ee58656d3"
   },
   "outputs": [],
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yCRyKvTbCpQW"
   },
   "source": [
    "## Log-binning\n",
    "\n",
    "One way to draw a histogram in log-scale, with a broadly distributed data, is by using log-binning. \n",
    "\n",
    "Let's first see what happens if we do not use the log scale for a dataset with a heavy tail.\n",
    "\n",
    "**Q: Load the movie dataset from `vega_datasets` and remove the NaN rows based on the following columns: `IMDB Rating`, `IMDB Votes`, `Worldwide_Gross`, `Rotten Tomatoes Rating`.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "0qBZGnGZCpQX"
   },
   "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>Title</th>\n",
       "      <th>US_Gross</th>\n",
       "      <th>Worldwide_Gross</th>\n",
       "      <th>US_DVD_Sales</th>\n",
       "      <th>Production_Budget</th>\n",
       "      <th>Release_Date</th>\n",
       "      <th>MPAA_Rating</th>\n",
       "      <th>Running_Time_min</th>\n",
       "      <th>Distributor</th>\n",
       "      <th>Source</th>\n",
       "      <th>Major_Genre</th>\n",
       "      <th>Creative_Type</th>\n",
       "      <th>Director</th>\n",
       "      <th>Rotten_Tomatoes_Rating</th>\n",
       "      <th>IMDB_Rating</th>\n",
       "      <th>IMDB_Votes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Slam</td>\n",
       "      <td>1009819.0</td>\n",
       "      <td>1087521.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1000000.0</td>\n",
       "      <td>Oct 09 1998</td>\n",
       "      <td>R</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Trimark</td>\n",
       "      <td>Original Screenplay</td>\n",
       "      <td>Drama</td>\n",
       "      <td>Contemporary Fiction</td>\n",
       "      <td>None</td>\n",
       "      <td>62.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>165.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Pirates</td>\n",
       "      <td>1641825.0</td>\n",
       "      <td>6341825.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>40000000.0</td>\n",
       "      <td>Jul 01 1986</td>\n",
       "      <td>R</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>Roman Polanski</td>\n",
       "      <td>25.0</td>\n",
       "      <td>5.8</td>\n",
       "      <td>3275.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Duel in the Sun</td>\n",
       "      <td>20400000.0</td>\n",
       "      <td>20400000.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6000000.0</td>\n",
       "      <td>Dec 31 2046</td>\n",
       "      <td>None</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>86.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>2906.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Tom Jones</td>\n",
       "      <td>37600000.0</td>\n",
       "      <td>37600000.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1000000.0</td>\n",
       "      <td>Oct 07 1963</td>\n",
       "      <td>None</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>81.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4035.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Oliver!</td>\n",
       "      <td>37402877.0</td>\n",
       "      <td>37402877.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10000000.0</td>\n",
       "      <td>Dec 11 1968</td>\n",
       "      <td>None</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Sony Pictures</td>\n",
       "      <td>None</td>\n",
       "      <td>Musical</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>84.0</td>\n",
       "      <td>7.5</td>\n",
       "      <td>9111.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Title    US_Gross  Worldwide_Gross  US_DVD_Sales  \\\n",
       "4              Slam   1009819.0        1087521.0           NaN   \n",
       "8           Pirates   1641825.0        6341825.0           NaN   \n",
       "9   Duel in the Sun  20400000.0       20400000.0           NaN   \n",
       "10        Tom Jones  37600000.0       37600000.0           NaN   \n",
       "11          Oliver!  37402877.0       37402877.0           NaN   \n",
       "\n",
       "    Production_Budget Release_Date MPAA_Rating  Running_Time_min  \\\n",
       "4           1000000.0  Oct 09 1998           R               NaN   \n",
       "8          40000000.0  Jul 01 1986           R               NaN   \n",
       "9           6000000.0  Dec 31 2046        None               NaN   \n",
       "10          1000000.0  Oct 07 1963        None               NaN   \n",
       "11         10000000.0  Dec 11 1968        None               NaN   \n",
       "\n",
       "      Distributor               Source Major_Genre         Creative_Type  \\\n",
       "4         Trimark  Original Screenplay       Drama  Contemporary Fiction   \n",
       "8            None                 None        None                  None   \n",
       "9            None                 None        None                  None   \n",
       "10           None                 None        None                  None   \n",
       "11  Sony Pictures                 None     Musical                  None   \n",
       "\n",
       "          Director  Rotten_Tomatoes_Rating  IMDB_Rating  IMDB_Votes  \n",
       "4             None                    62.0          3.4       165.0  \n",
       "8   Roman Polanski                    25.0          5.8      3275.0  \n",
       "9             None                    86.0          7.0      2906.0  \n",
       "10            None                    81.0          7.0      4035.0  \n",
       "11            None                    84.0          7.5      9111.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mHesgk87CpQX"
   },
   "source": [
    "If you simply call `hist()` method with a dataframe object, it identifies all the numeric columns and draw a histogram for each.\n",
    "\n",
    "**Q: draw all possible histograms of the movie dataframe. Adjust the size of the plots if needed.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "9ob4iXNCCpQX",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "4b246a8b-a97a-4a5d-deab-7f831acd8906"
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x1000 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2mEruHmQCpQY"
   },
   "source": [
    "As we can see, a majority of the columns are not normally distributed. In particular, if you look at the worldwide gross variable, you only see a couple of meaningful data from the histogram. Is this a problem of resolution? How about increasing the number of bins?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "RxgQU5phCpQY",
    "outputId": "1e350dc9-2099-4219-a8ff-96200b4f7a20"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Frequency')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jjz8uH3zwgVy+fNn3rQIAAPBn2Nm8ebPcd999Eh8fL9HR0fLHP/5RNm7c6Ks2AQAA+DfsxMTEyMSJE+XYsWMyY8YMOX78uDRp0kRq164t48aNk59++sl3LQQAAPDXBOWwsDDp2LGjzJs3T8aMGSP79u2TV155RSpWrCjPP/+8CUEAAAD5Nuxs2rRJ/vznP0u5cuVMj44Gnf3798vy5ctNr0+7du1811IAAIBcCMvNgzTYzJw5U/bs2SNt2rSR999/39yGhv5fdqpatarMmjVLqlSpkpunBwAA8G/YmTJlivzXf/2XdO/e3fTqZKZMmTIyffp0b9sHAABw68PO3r17b7hPwYIFJS4uLjdPDwAA4N85OzqEpZOS09N1s2fP9kW7AAAAfCJXYSchIUFuu+22TIeuXn/9dV+0CwAAwH9h5/Dhw2YScnqVK1c22wAAAPJ12NEenG3btmVY/91330np0qV90S4AAAD/hZ1nnnlGXnrpJVm5cqVcv37dLCtWrJC+fftKly5dfNMyAAAAfx2NNWrUKPnhhx+kWbNm5izKKjU11Zw1mTk7AAAg34cdPaz8o48+MqFHh64KFSokderUMXN2AAAA8n3YcbnnnnvMAgAAYFXY0Tk6ejmIxMRESU5ONkNYaen8HQAAgHwbdnQisoadtm3bSu3atSUkJMT3LQMAAPBX2Jk7d658/PHH5uKfAAAA1h16rhOUq1Wr5vvWAAAABELYefnll2XixIniOI6v22OtKoMWuxcAABDgw1hff/21OaHgF198IbVq1ZLw8HCP7Z988omv2gcAAHDrw07JkiWlQ4cO3r0yAABAoIadmTNn+r4lAAAAgTJnR127dk2++uormTZtmpw/f96sO3bsmFy4cMGX7QMAALj1PTuHDh2SVq1ayeHDhyUlJUVatGghxYoVkzFjxpj7U6dO9a5VAAAA/uzZ0ZMK1q9fX06fPm2ui+Wi83j0rMoAAAD5umfnX//6l6xbt86cbyetKlWqyI8//uirtgEAAPinZ0evhaXXx0rv6NGjZjgLAAAgX4edli1byoQJE9z39dpYOjF52LBhXEICAADk/7Dz1ltvydq1a6VmzZpy+fJlefbZZ91DWDpJ+WZNmTJF7rvvPilevLhZGjVqZE5U6KLP3atXLyldurQULVpUOnXqJCdPnvR4Dp0krRckLVy4sJQpU0YGDBhgjhQDAADI9ZydChUqyHfffWcuCLpt2zbTq9OjRw/p2rWrx4Tlm3meN954Q+6++25z6YnZs2dLu3btZMuWLebMzP3795fFixfLvHnzpESJEtK7d2/p2LGjCVpKh9I06ERHR5s5RMePH5fnn3/enNH59ddf528YAADkLuyYB4aFyXPPPefViz/55JMe9//617+a3p4NGzaYIDR9+nSZM2eOPPHEE+6TGdaoUcNsb9iwoSxbtkx27dplzvdTtmxZiYmJkVGjRsmrr74qw4cPzzCBGgAABJ9chZ33338/2+3au5JT2kujPTgXL140w1lJSUly9epVad68uXuf6tWrS6VKlWT9+vUm7OhtnTp1TNBxiY2NlZ49e8rOnTulbt26mb6WngtIF5dz586ZW309XXzF9VwRoZ4XTPXlawQDV72oW+5RQ9+gjt6jht6jhr+52RqE5fY8O+lf7NKlS6YnRefO5CTsbN++3YQbnZ+j83IWLFhg5gJt3brVPJ9ehystDTYnTpwwP+tt2qDj2u7alpWEhAQZMWJEhvXaU6Tt97VR9VM97i9ZssTnrxEMli9f7u8m5HvU0Deoo/eoofeooZjskWdhR08mmN7evXtNj4pOEM6Je++91wSbs2fPyj//+U+Ji4uT1atXS14aPHiwxMfHe/TsVKxY0RxlphOlfUVDoH4YX9sUKimpIe71O4bH+uw1goGrjnqmbp2PhZyjhr5BHb1HDb1HDSXDyEyezdlJTycZ62Rjncfz73//+6Yfp7031apVMz/Xq1dPvv32W5k4caJ07txZrly5ImfOnPHo3dGjsXRCstLbjRs3ejyf62gt1z6ZiYiIMEt6+qHJiw+OBp2U67+FnWD/cOZWXv39BBNq6BvU0XvU0HvUUG76/ef6QqBZTVrWi4F6Q09YqPNpNPjom0h7+Yk9e/aYQ8112EvprQ6DJScnu/fRtKu9MzoUBgAAkKuenc8++8zjvh42rod9v/vuu9K4ceMcDSe1bt3aTDrWK6frkVerVq2SL7/80hxqroez63BTVFSUCTB9+vQxAUcnJysddtJQ061bNxk7dqyZpzNkyBBzbp7Mem4AAEDwyVXYad++vcd9PYPy7bffbg4R1xMO3iztkdHJzBqUNNzoCQY16Og4pBo/fryEhoaakwlqb48eaTV58mT34wsUKCCLFi0yc4U0BBUpUsTM+Rk5cmRu3hYAALBQWG6HmnxBz6OTncjISJk0aZJZslK5cmWObgIAALdmzg4AAIAVPTtpD9u+kXHjxuXmJQAAAPwXdvTaVbrosf56nhz1/fffmzk0DzzwgMdcHgAAgHwXdvSaVsWKFTMX7ixVqpT7RIO///3v5ZFHHpGXX37Z1+0EAAC4dXN29IgrveSCK+go/Xn06NE5OhoLAAAgIMOOnp75p59+yrBe1+n5cgAAAPJ12OnQoYMZsvrkk0/k6NGjZpk/f745CWDHjh1930oAAIBbOWdn6tSp8sorr8izzz7rvry6XipCw87f/va33LYFAAAgMMJO4cKFzZmMNdjs37/frLvrrrvMGYwBAACsOamgXuZBF73iuQYdvUYWAABAvg87v/zyizRr1kzuueceadOmjQk8SoexOOwcAAAEklyFnf79+0t4eLgcPnzYDGm5dO7cWZYuXerL9gEAANz6OTvLli0zVyevUKGCx3odzjp06JB3LQIAAPB3z87Fixc9enRcTp06JREREb5oFwAAgP/Cjl4S4v333/e4BlZqaqqMHTtWHn/8cd+0DAAAwF/DWBpqdILypk2b5MqVKzJw4EDZuXOn6dlZu3atL9oFAADgv56d2rVrm6ucN2nSRNq1a2eGtfTMyXoldD3fDgAAQL7t2dEzJrdq1cqcRfm///u/86ZVAAAA/urZ0UPOt23b5qvXBwAACLxhrOeee06mT5/u+9YAAAAEwgTla9euyYwZM+Srr76SevXqZbgm1rhx43zVPgAAgFsXdg4cOCBVqlSRHTt2yAMPPGDW6UTltPQwdAAAgHwZdvQMyXodrJUrV7ovD/H2229L2bJl86p9AAAAt27OTvqrmn/xxRfmsHMAAACrJihnFX4AAADyddjR+Tjp5+QwRwcAAFgzZ0d7crp37+6+2Ofly5flT3/6U4ajsT755BPfthIAAOBWhJ24uLgM59sBAACwJuzMnDkz71oCAAAQaBOUAQAAAh1hBwAAWI2wAwAArEbY8YMqgxabBQAA5D3CDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALCaX8NOQkKCPPjgg1KsWDEpU6aMtG/fXvbs2eOxz+XLl6VXr15SunRpKVq0qHTq1ElOnjzpsc/hw4elbdu2UrhwYfM8AwYMkGvXrt3idwMAAAKRX8PO6tWrTZDZsGGDLF++XK5evSotW7aUixcvuvfp37+/fP755zJv3jyz/7Fjx6Rjx47u7devXzdB58qVK7Ju3TqZPXu2zJo1S4YOHeqndwUAAAJJmD9ffOnSpR73NaRoz0xSUpI8+uijcvbsWZk+fbrMmTNHnnjiCbPPzJkzpUaNGiYgNWzYUJYtWya7du2Sr776SsqWLSsxMTEyatQoefXVV2X48OFSsGDBDK+bkpJiFpdz586ZWw1buviK67kiQp1styN7rjpRr9yjhr5BHb1HDb1HDX9zszUIcRwn89/EfrBv3z65++67Zfv27VK7dm1ZsWKFNGvWTE6fPi0lS5Z071e5cmXp16+f6fXRHpzPPvtMtm7d6t5+8OBBufPOO2Xz5s1St27dDK+jIWjEiBEZ1muo0qEwAAAQ+C5duiTPPvus6RwpXrx4YPbspJWammoCTOPGjU3QUSdOnDA9M2mDjtIeHN3m2kfvp9/u2paZwYMHS3x8vEfPTsWKFc0QWnbFyk3i1OG51zaFSkpqSIbtO4bH+uy1bOaqY4sWLSQ8PNzfzcmXqKFvUEfvUUPvUUPJMDJzIwETdnTuzo4dO+Trr7/O89eKiIgwS3r6ocmLD44GnZTrGcNOsH9Icyqv/n6CCTX0DeroPWroPWooN/3+A+LQ8969e8uiRYtk5cqVUqFCBff66OhoM/H4zJkzHvvr0Vi6zbVP+qOzXPdd+wAAgODl17Cj04U06CxYsMDMz6latarH9nr16pnUlpiY6F6nh6broeaNGjUy9/VW5/gkJye799HuPR2Oqlmz5i18NwAAIBCF+XvoSicFf/rpp+ZcO645NiVKlJBChQqZ2x49epj5NVFRUSbA9OnTxwQcPRJL6TwbDTXdunWTsWPHmucYMmSIee7MhqoAAEBw8WvYmTJlirlt2rSpx3o9vLx79+7m5/Hjx0toaKg5maAeLh4bGyuTJ09271ugQAEzBNazZ08TgooUKSJxcXEycuTIW/xuAABAIPJr2LmZo94jIyNl0qRJZsmKHoq+ZMkSH7cOAADYICAmKAMAAOQVwg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbY8aMqgxabBQAA5B3CDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCTgCoMmixWQAAgO8RdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNb+GnTVr1siTTz4p5cuXl5CQEFm4cKHHdsdxZOjQoVKuXDkpVKiQNG/eXPbu3euxz6lTp6Rr165SvHhxKVmypPTo0UMuXLhwi98JAAAIVH4NOxcvXpT7779fJk2alOn2sWPHyttvvy1Tp06Vb775RooUKSKxsbFy+fJl9z4adHbu3CnLly+XRYsWmQD14osv3sJ3AQAAAlmYP1+8devWZsmM9upMmDBBhgwZIu3atTPr3n//fSlbtqzpAerSpYvs3r1bli5dKt9++63Ur1/f7PPOO+9ImzZt5M033zQ9RgAAILj5Nexk5+DBg3LixAkzdOVSokQJadCggaxfv96EHb3VoStX0FG6f2hoqOkJ6tChQ6bPnZKSYhaXc+fOmdurV6+axVdczxUR6uRof2ReF+qTe9TQN6ij96ih96jhb262BgEbdjToKO3JSUvvu7bpbZkyZTy2h4WFSVRUlHufzCQkJMiIESMyrF+2bJkULlxYfG1U/dSb2m/JkiU+f22b6FAlvEMNfYM6eo8aeo8aily6dCl/h528NHjwYImPj/fo2alYsaK0bNnSTHT2ZeLUD+Nrm0IlJTXkhvvvGB7rs9e2iauOLVq0kPDwcH83J1+ihr5BHb1HDb1HDSXDyEy+DTvR0dHm9uTJk+ZoLBe9HxMT494nOTnZ43HXrl0zR2i5Hp+ZiIgIs6SnH5q8+OBo0Em5fuOwE+wf2hvJq7+fYEINfYM6eo8aeo8ayk2//4A9z07VqlVNYElMTPRIcDoXp1GjRua+3p45c0aSkpLc+6xYsUJSU1PN3B4AAAC/9uzo+XD27dvnMSl569atZs5NpUqVpF+/fjJ69Gi5++67Tfh57bXXzBFW7du3N/vXqFFDWrVqJS+88II5PF279nr37m0mL+fHI7GqDFrs/vmHN9r6tS0AANjCr2Fn06ZN8vjjj7vvu+bRxMXFyaxZs2TgwIHmXDx63hztwWnSpIk51DwyMtL9mA8//NAEnGbNmpmjsDp16mTOzQMAAOD3sNO0aVNzPp2s6FmVR44caZasaC/QnDlz8qiFAAAgvwvYOTsAAAC+QNgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsJMPLiGR9jISAAAgZwL2qufBjoADAIBv0LMDAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7FhwjSyunwUAQNYIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1cL83QDkTNqTB/7wRlu/tgUAgPyAnh0AAGA1enbyMS4RAQDAjdGzYzmumwUACHaEHQAAYDWGsSxFbw4AAP+HsGMRAg4AABkxjAUAAKxG2AEAAFYj7AAAAKsRdgAAgNUIO0GC8+0AAIIVYQcAAFiNsBPE6O0BAAQDzrMTZLILN5lt48rqAID8jrADn/XuuJ6HgAQACCSEHXgdZBgKAwAEMubsAAAAq9Gzg2yl77WhFwcAkN/QswMAAKxG2EHAHNKe/nEcGg8A8AVrws6kSZOkSpUqEhkZKQ0aNJCNGzf6u0lBzxVWCDAAAH+yYs7ORx99JPHx8TJ16lQTdCZMmCCxsbGyZ88eKVOmjL+bhxzO/cnJNg5zBwAERdgZN26cvPDCC/L73//e3NfQs3jxYpkxY4YMGjTI381DgBwunzYo5XVIupWvBQCwPOxcuXJFkpKSZPDgwe51oaGh0rx5c1m/fn2mj0lJSTGLy9mzZ83tqVOn5OrVqz5rmz7XpUuXJOxqqFxPDfHZ8wabX375xdRRb8OuXfTYVu2Vj2/44Xbtk/bD7lr3zeBmHo9pkJCY4Xlc+2S27Uavndlr5fY1cvL49O/L9VnUGjZ5c02Wz3ej5wl2aesYHh4utrkVf++21/BWyE81bJDHn6nz58+bW8dxst/Ryed+/PFHfYfOunXrPNYPGDDAeeihhzJ9zLBhw8xjWFhYWFhYWCTfL0eOHMk2K+T7np3c0F4gnePjkpqaanp1SpcuLSEhvuuBOXfunFSsWFGOHDkixYsX99nzBhvq6D1q6BvU0XvU0HvU8Dfao6O9O+XLl5fs5Puwc9ttt0mBAgXk5MmTHuv1fnR0dKaPiYiIMEtaJUuWzLM26ocx2D+QvkAdvUcNfYM6eo8aeo8a/p8SJUqI9YeeFyxYUOrVqyeJiYkePTV6v1GjRn5tGwAA8L9837OjdEgqLi5O6tevLw899JA59PzixYvuo7MAAEDwsiLsdO7cWX766ScZOnSonDhxQmJiYmTp0qVStmxZv7ZLh8qGDRuWYcgMOUMdvUcNfYM6eo8aeo8a5lyIzlLOxeMAAADyhXw/ZwcAACA7hB0AAGA1wg4AALAaYQcAAFiNsOOlSZMmSZUqVSQyMtJccX3jxo3Z7j9v3jypXr262b9OnTqyZMmSW9ZWW+o4a9Ysc6brtIs+LpitWbNGnnzySXMWUa3HwoULb/iYVatWyQMPPGCO6KhWrZqpazDLaQ21fuk/h7roEaHBKiEhQR588EEpVqyYlClTRtq3by979uy54eP4XvS+jnwvZo+w44WPPvrInONHDwHcvHmz3H///RIbGyvJycmZ7r9u3Tp55plnpEePHrJlyxbzAdZlx44dEsxyWkelZw09fvy4ezl06JAEMz2vlNZNQ+PNOHjwoLRt21Yef/xx2bp1q/Tr10/+8Ic/yJdffinBKqc1dNFfQmk/i/rLKVitXr1aevXqJRs2bJDly5ebC1a2bNnS1DYrfC/6po6K78Vs+PKinMFGLzTaq1cv9/3r16875cuXdxISEjLd/+mnn3batm3rsa5BgwbOH//4RyeY5bSOM2fOdEqUKHELW5i/6D/rBQsWZLvPwIEDnVq1anms69y5sxMbG5vHrbOnhitXrjT7nT59+pa1K79JTk42NVq9enWW+/C96Js68r2YPXp2cunKlSuSlJQkzZs3d68LDQ0199evX5/pY3R92v2V9mBktX8wyE0d1YULF6Ry5crmYnjt2rWTnTt33qIW24HPou/oSUzLlSsnLVq0kLVr1/q7OQHl7Nmz5jYqKirLffgs+qaOiu/FrBF2cunnn3+W69evZzhLs97Pasxe1+dk/2CQmzree++9MmPGDPn000/lgw8+MNdCe/jhh+Xo0aO3qNX5X1afRb2a8q+//uq3duUnGnCmTp0q8+fPN4v+gmnatKkZisX/XaNQh0cbN24stWvXznI/vhd9U0e+F4PgchEILnqB17QXedV/0DVq1JBp06bJqFGj/No2BA/95aJL2s/h/v37Zfz48fKPf/xDgp3OOdF5N19//bW/mxIUdeR7MXv07OTSbbfdJgUKFJCTJ096rNf70dHRmT5G1+dk/2CQmzqmFx4eLnXr1pV9+/blUSvtk9VnUSc4FipUyG/tyu/0QsR8DkV69+4tixYtkpUrV0qFChWy3ZfvRd/UMT2+Fz0RdnKpYMGCUq9ePUlMTHSv025DvZ82Xael69Pur3SmfVb7B4Pc1DE9HQbbvn27GVbAzeGzmDf0yLZg/hzq3G79Bb1gwQJZsWKFVK1a9YaP4bPomzqmx/diOjeYwIxszJ0714mIiHBmzZrl7Nq1y3nxxRedkiVLOidOnDDbu3Xr5gwaNMi9/9q1a52wsDDnzTffdHbv3u0MGzbMCQ8Pd7Zv3+4Es5zWccSIEc6XX37p7N+/30lKSnK6dOniREZGOjt37nSC1fnz550tW7aYRf9Zjxs3zvx86NAhs13rp3V0OXDggFO4cGFnwIAB5rM4adIkp0CBAs7SpUudYJXTGo4fP95ZuHChs3fvXvNvuG/fvk5oaKjz1VdfOcGqZ8+e5oigVatWOcePH3cvly5dcu/D92Le1JHvxewRdrz0zjvvOJUqVXIKFixoDqHesGGDe9tjjz3mxMXFeez/8ccfO/fcc4/ZXw/9Xbx4sR9anb/r2K9fP/e+ZcuWddq0aeNs3rzZCWauw6DTL6666a3WMf1jYmJiTB3vvPNOc+hqMMtpDceMGePcdddd5hdKVFSU07RpU2fFihVOMMusfrqk/WzxvZg3deR7MXsh+kf63h4AAABbMGcHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQdAnhs+fLjExMRku0/37t2lffv2PnvNkJAQWbhwYZbbf/jhB7OPXs8KQN5Ys2aNPPnkk1K+fPkb/pvMyscff2y+PwoXLiyVK1eWv/3tbzl+DsIOEISmTp0qxYoVk2vXrrnXXbhwwVwpuWnTph77rlq1ynxJ7d+/X/KT48ePS+vWrf3dDCCoXbx4Ue6//36ZNGlSrh7/xRdfSNeuXeVPf/qT7NixQyZPnizjx4+Xd999N0fPQ9gBgtDjjz9uws2mTZvc6/71r39JdHS0fPPNN3L58mX3+pUrV0qlSpXkrrvuyvHr6NVo0gaqW0nfS0REhASaK1eu+LsJwC2j/+EYPXq0dOjQIdPtKSkp8sorr8gdd9whRYoUkQYNGpj/YLn84x//MD2+GnbuvPNOadu2rQwePFjGjBljvl9uFmEHCEL33nuvlCtXzuNLRX9u166dVK1aVTZs2OCxXsOR64vppZdekjJlykhkZKQ0adJEvv322wy9QPq/sXr16pmw8fXXX2d4/evXr0t8fLyULFlSSpcuLQMHDsz2i0u33X777fLPf/7TvU67tfU9uOjr6OtdunTJ3E/fZb5x40apW7euaXf9+vVly5YtGV5H/+eoX85FixaVsmXLSrdu3eTnn3/OtpbvvfeeVKxY0XSx6xf6uHHjzPtKP4T3P//zP6a2+vrq8OHDpt76WsWLF5enn35aTp486X7cd999Z+quPXC6XevpCqeHDh0yQwOlSpUyvyBq1aolS5YsybadQCDq3bu3rF+/XubOnSvbtm2Tp556Slq1aiV79+51f+e4/s24FCpUSI4ePWr+Hdwswg4QpPQXqfbauOjPOoT12GOPudf/+uuvpqfHFXY0lMyfP19mz54tmzdvlmrVqklsbKycOnXK47kHDRokb7zxhuzevVvuu+++DK/91ltvyaxZs2TGjBkmpOjjFyxYkGVbNbg8+uij7nB2+vRp89zavn//+99m3erVq+XBBx80oSM97cX63e9+JzVr1pSkpCQTQPR/k2mdOXNGnnjiCROINFQsXbrUhA8NIVlZu3at+R9n3759zdyfFi1ayF//+tcM++3bt8/U7ZNPPjH7paammqCj71vbvXz5cjlw4IB07tzZ/Rjtuq9QoYIJk9pmrakOM6pevXqZXwI6H2L79u3mf7kamoD85PDhwzJz5kyZN2+ePPLII6b3WP9d6n+idL3S7xf9d5OYmGj+3Xz//ffm+8M1VH3TbnBVdACWeu+995wiRYo4V69edc6dO+eEhYU5ycnJzpw5c5xHH33U7JOYmKjdLc6hQ4ecCxcuOOHh4c6HH37ofo4rV6445cuXd8aOHWvur1y50uy/cOFCj9caNmyYc//997vvlytXzv0YpW2oUKGC065duyzb+/bbbzu1atUyP+vzN2jQwOw/ZcoUs6558+bOX/7yF/f+2o4FCxaYn6dNm+aULl3a+fXXX93b9XG6z5YtW8z9UaNGOS1btvR4zSNHjph99uzZk2mbOnfu7LRt29ZjXdeuXZ0SJUp4vHetm9bWZdmyZU6BAgWcw4cPu9ft3LnTvNbGjRvN/WLFijmzZs3K9HXr1KnjDB8+PMtaAYFI0vybVIsWLTLr9Hso7aLfRU8//bTZJzU11Rk4cKATGRlp/s2UKlXKfPb1cRs2bLjp16ZnBwhS2oujkwe150Dn69xzzz1mqEh7dlzzdrQnRcfJdc6OTlC+evWqNG7c2P0c2tPw0EMPmV6WtHSYKCtnz541/yPTsXmXsLCwbB+jtF27du2Sn376yfSGaPt10TZqu9atW5dhcrWLq4cpbXd4o0aNPPbRYSPt0dIeEtdSvXp1sy2rydl79uwx7z+t9PeVHkGitU3bHh360sVFe510+MtVSx3m+8Mf/iDNmzc3vWRp26BDiToPQv8uhg0bZrr/gfzmwoULUqBAAdNzqT2erkX/DUycONHdq6s9l7qvDludOHHC/W9Mv5tuFmEHCFI6BKXDJPoLXhcNE0oPEdVfwhoedL0O7eSUziPxtTp16khUVJQJOmnDjv6sgU0Dz8MPP5zr59cvU50Hk/ZLVxedO6BDaN7ITT10qG3nzp1mQuaKFStMGHIN9WkI0mEvnVOkw1gaFN955x2v2gjcajpkrPP3kpOTzfdR2kUPMEhLQ5FOYi5YsKD87//+r/nPStr/QNwIYQcIYjoXR3tGdEnbK6K/3HWSsU7qdc3X0fF0/aLReSouGjA0aOgv4ptVokQJM7FYe49c9Igt/d9ddvR/eDqu/+mnn5oQoOP62lujc1emTZtmfuFnFSpq1Khhej/SHmWWdhK2euCBB8zzVqlSJcMXb1bPqxO9007QVunvZ9WeI0eOmMVFe6103lDaWmpvW//+/WXZsmXSsWNH9zwGpYFU5wvpfIaXX37ZTJQGAs2FCxfc/3FQBw8eND/rfB39fOvctOeff958jnWbfuckJCTI4sWLzf56gICeKkPn5unjdH6czvGZMGFCzhqSJwNzAPKFGTNmOIUKFTJj5CdOnHCvnz17tpkzol8Rx44dc6/v27evmaPzxRdfmDkmcXFxZgz91KlTHnN2Tp8+ne2cnTfeeMOJiooy4/e7d+92XnjhBfN62c3ZURMmTDDj9jpfx0Ufo+sGDRqU5fyA8+fPO7fddpvz3HPPmXYvXrzYqVatmsecnR9//NG5/fbbnf/8z/8082b27dvnLF261Onevbtz7dq1TNvz9ddfO6Ghoc5bb73lfP/9987UqVPN3KCSJUtm+d5d8xBiYmKcRx55xElKSnK++eYbp169es5jjz1mtl+6dMnp1auXqecPP/xgXueuu+4ycxdcfw/atgMHDpjHaz1ccxyAQLLy/38npF/0u8M172/o0KFOlSpVzNw2nc/XoUMHZ9u2bWb7Tz/95DRs2NDM5SlcuLDTrFmzHM3VcSHsAEHs4MGD5ounevXqHuv1F6yuv/feez3W6wTfPn36mOAQERHhNG7c2D2hNidhRyck6y/s4sWLm2AQHx/vPP/88zcMOxpM9PlfffVV97rx48ebdfrLP7vJkOvXrzdtKFiwoAka8+fP9wg7SgOLftFqmzQEal369etnwklW/v73vzt33HGH2b99+/bO6NGjnejo6Czfu4tO+v6P//gP8yWuQe+pp55yB86UlBSnS5cuTsWKFU17NWD27t3bPcFaf9bwo38HGtC6devm/Pzzz9nWDghmIfpHXnRdAUAweuGFF0yXu076BhAYwvzdAADIz958801zfh2d16PznPQcRHpKewCBg54dAPCCnnRQJ3ifP3/eHArbp08fM3EYQOAg7AAAAKtx6DkAALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAIDb7f+Z8IfPjOit+AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = movies[\"Worldwide_Gross\"].hist(bins=200)\n",
    "ax.set_xlabel(\"World wide gross\")\n",
    "ax.set_ylabel(\"Frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0b-eOpyCCpQY"
   },
   "source": [
    "Maybe a bit more useful, but it doesn't tell anything about the data distribution above certain point. How about changing the vertical scale to logarithmic scale?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "AOriHl4PCpQY",
    "outputId": "33df417f-1d38-452f-f265-ac6e3f0c52ee"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Frequency')"
      ]
     },
     "execution_count": 8,
     "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": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TkNpbIB8CpQY"
   },
   "source": [
    "Now, let's try log-bin. Recall that when plotting histgrams we can specify the edges of bins through the `bins` parameter. For example, we can specify the edges of bins to [1, 2, 3, ... , 10] as follows.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "UWM6cu3HCpQZ",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "77c5f8b4-d193-4def-a66d-fc7c55a3b9bf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 9,
     "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": [
    "movies[\"IMDB_Rating\"].hist(bins=range(0,11))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "U68yd_uXCpQZ"
   },
   "source": [
    "Here, we can specify the edges of bins in a similar way. Instead of specifying on the linear scale, we do it on the log space. Some useful resources:\n",
    "\n",
    "* [Google query: python log-bin](https://www.google.com/search?q=python+log+binning)\n",
    "* [numpy.logspace](https://numpy.org/doc/stable/reference/generated/numpy.logspace.html)\n",
    "* [numpy.linspace vs numpy.logspace](https://stackoverflow.com/questions/31480033/difference-in-output-between-numpy-linspace-and-numpy-logspace)\n",
    "\n",
    "Hint: since $10^{\\text{start}}= \\text{min(Worldwide\\_Gross)}$, $\\text{start} = \\log_{10}(\\text{min(Worldwide\\_Gross)})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "Fmp9ZabECpQZ",
    "outputId": "b50c35b8-8b1c-4dae-f5c7-c5fe83f0a0e0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(movies[\"Worldwide_Gross\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "A8SDO_EJCpQZ"
   },
   "source": [
    "Because there seems to be movie(s) that made $0, and because log(0) is undefined & log(1) = 0, let's add 1 to the variable.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "SbhRBP1tCpQZ"
   },
   "outputs": [],
   "source": [
    "movies[\"Worldwide_Gross\"] = movies[\"Worldwide_Gross\"]+1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 78,
     "status": "ok",
     "timestamp": 1666625970622,
     "user": {
      "displayName": "Devin Wright",
      "userId": "04589681907982391901"
     },
     "user_tz": 240
    },
    "id": "gfdSnM4LCpQa",
    "outputId": "6a9f01db-7a92-4998-d103-a9c48935db66"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+00, 3.14018485e+00, 9.86076088e+00, 3.09646119e+01,\n",
       "       9.72346052e+01, 3.05334634e+02, 9.58807191e+02, 3.01083182e+03,\n",
       "       9.45456845e+03, 2.96890926e+04, 9.32292387e+04, 2.92757043e+05,\n",
       "       9.19311230e+05, 2.88680720e+06, 9.06510822e+06, 2.84661155e+07,\n",
       "       8.93888645e+07, 2.80697558e+08, 8.81442219e+08, 2.76789150e+09])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: specify the edges of bins using np.logspace\n",
    "\n",
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PIqzy3kVCpQa"
   },
   "source": [
    "Now we can plot a histgram with log-bin. Set both axis to be log-scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "cxA8ouz3CpQa",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "305ad2e2-eaa8-4252-b38f-acd9cb6e7232"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Frequency')"
      ]
     },
     "execution_count": 13,
     "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": [
    "ax = (movies[\"Worldwide_Gross\"]+1.0).hist(bins=bins)\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel(\"World wide gross\")\n",
    "ax.set_ylabel(\"Frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bqvIISFeCpQa"
   },
   "source": [
    "What is going on? Is this the right plot?\n",
    "\n",
    "**Q: explain and fix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "6RCM81QBCpQa",
    "jupyter": {
     "outputs_hidden": false
    },
    "outputId": "57fe4ceb-0246-4f09-fdb1-c1b87c8c03d1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability density')"
      ]
     },
     "execution_count": 14,
     "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": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive exploration of log-binning\n",
    "\n",
    "Let's put the linear and log-binned histogram side by side to explore how the number of bins affects the log-binned histogram visualization. The slider below allows you to experiment with different numbers of bins to see how it impacts the visualization of the heavy-tailed distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e5d3863ad1ed4a33849dcd51689aee7d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=50, description='n_bins', min=5, step=5), Output()), _dom_classes=('widg…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "@interact(n_bins=(5, 100, 5))\n",
    "def plot_log_histogram(n_bins):\n",
    "    \"\"\"\n",
    "    Interactive visualization to explore how bin number affects log-binned histograms.\n",
    "    \n",
    "    Parameters:\n",
    "    n_bins: Number of bins for the histogram\n",
    "    \"\"\"\n",
    "\n",
    "    # Create linear-spaced bins\n",
    "    linear_bins = np.linspace(movies[\"Worldwide_Gross\"].min(), movies[\"Worldwide_Gross\"].max(), n_bins)\n",
    "\n",
    "    # Create log-spaced bins\n",
    "    log_bins = np.logspace(np.log10(movies[\"Worldwide_Gross\"].min()), \n",
    "                      np.log10(movies[\"Worldwide_Gross\"].max()), \n",
    "                      n_bins)\n",
    "    \n",
    "    # Create figure with two subplots\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))\n",
    "    \n",
    "    # Left plot: Linear scale\n",
    "    ax1.hist(movies[\"Worldwide_Gross\"], bins=linear_bins, density=True, alpha=0.7, color='blue', edgecolor='black')\n",
    "    ax1.set_xlabel(\"Worldwide Gross Revenue ($)\")\n",
    "    ax1.set_ylabel(\"Probability Density\")\n",
    "    ax1.set_title(f\"Linear Scale (n_bins={n_bins})\")\n",
    "    ax1.grid(True, alpha=0.3)\n",
    "    \n",
    "    # Right plot: Log-log scale\n",
    "    ax2.hist(movies[\"Worldwide_Gross\"], bins=log_bins, density=True, alpha=0.7, color='green', edgecolor='black')\n",
    "    ax2.set_xscale('log')\n",
    "    ax2.set_yscale('log')\n",
    "    ax2.set_xlabel(\"Worldwide Gross Revenue ($, log scale)\")\n",
    "    ax2.set_ylabel(\"Probability Density (log scale)\")\n",
    "    ax2.set_title(f\"Log-Log Scale (n_bins={n_bins})\")\n",
    "    ax2.grid(True, which=\"both\", ls=\"-\", alpha=0.2)\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5QcCWTBrCpQb"
   },
   "source": [
    "## CCDF\n",
    "\n",
    "The cumulative distribution function $F_X(x)$ at $x$ is defined by \n",
    "\n",
    "$$F_X(x) = P(X \\le x),$$ \n",
    "\n",
    "which is, in other words, the probability that $X$ takes a value less than or equal to $x$. When empirically calculated (empirical CDF), $F_X(x)$ is the fraction of data points that are less than or equal to $x$. CDF allows us to examine any percentile of the data distribution and is also useful for comparing distributions. \n",
    "\n",
    "However, when the data spans multiple orders of magnitude, CDF may not be useful. Let's try. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gross_sorted = movies.Worldwide_Gross.sort_values()\n",
    "N = len(gross_sorted)\n",
    "Y = np.linspace(1/N, 1, num=N)\n",
    "plt.xlabel(\"World wide gross\")\n",
    "plt.ylabel(\"Empirical CDF\")\n",
    "_ = plt.plot(gross_sorted, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although the movies that are interesting are those with large worldwide gross, we don't see any details about their distribution as they are all close to 1. In other words, CDF sucks at revealing the details of the tail."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CCDF is a nice alternative to examine distributions with heavy tails. The idea is same as CDF, but the direction of aggregation is opposite. Because we are starting from the largest value, it can reveal the details of those large values (tail). \n",
    "\n",
    "CCDF is defined as follows:\n",
    "\n",
    "$$ \\bar{F}_X(x) = P(X > x)$$\n",
    "\n",
    "And thus, \n",
    "\n",
    "$$ \\bar{F}_X(x) = P(X > x) = 1 - F_X(x)$$\n",
    "\n",
    "In other words, we can use CDF to calculate CCDF.\n",
    "\n",
    "**Q: draw CCDF using the CDF code above.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How about making the y axis in log scale?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although this is technically the correct CCDF plot, there is a very subtle issue. Do you see the vertical line at the rightmost side of the CCDF plot? To understand what's going on, let's look at the Y values of this plot. We used 1 - CDF to calculate CCDF. So,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.99556738e-01, 9.99113475e-01, 9.98670213e-01, ...,\n",
       "       8.86524823e-04, 4.43262411e-04, 0.00000000e+00], shape=(2256,))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens when we take the log of these values?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/d0/wgh1l_5905x4crqpp1b7whz40000gn/T/ipykernel_8464/1767632406.py:1: RuntimeWarning: divide by zero encountered in log\n",
      "  np.log(1-Y)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-4.43360681e-04, -8.86918018e-04, -1.33067219e-03, ...,\n",
       "       -7.02820143e+00, -7.72134861e+00,            -inf], shape=(2256,))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(1-Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the last value of 1 - Y is 0.0, we got `-inf` as the log value. That means, the largest value's (let's say $x$) coordinate in our CCDF plot will be $(x, -inf)$ if we use a log scale for our y-axis. And thus we will not be able to see it in the plot. This occurs because we are drawing CDF in a simplified way. In reality, ECDF and ECCDF are step functions and this shouldn't matter. However, because we are drawing a line between the points, we are getting this issue.\n",
    "\n",
    "This is somewhat problematic because the largest value in our dataset can be quite important and therefore we want to see it in the plot! \n",
    "\n",
    "This is why, in practice, we sometimes use \"incorrect\" version of CCDF. We can consider $\\bar{F}_X(x)$ as a \"flipped\" version of CDF. \n",
    "\n",
    "$$ \\bar{F}_X(x) = P(X \\ge x) $$\n",
    "\n",
    "instead of \n",
    "\n",
    "$$ \\bar{F}_X(x) = P(X > x) $$\n",
    "\n",
    "In doing so, we can see the largest value in the data in our CCDF plot. We can also draw the correct version of CCDF, but this quick-and-dirty version is often easier and good enough to show what we want to show. \n",
    "\n",
    "A simple way is just to define the y coordinates as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = np.linspace( 1.0, 1/N, num=N)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q: Draw a CCDF of worldwide gross data. Use log scale for y-axis.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "BY_idtbfCpQb",
    "outputId": "7650fed1-1d6e-4dbe-d363-b654046a9aed"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "s8adn3TOCpQb"
   },
   "source": [
    "A straight line in semilog scale means exponential decay (cf. a straight line in log-log scale means power-law decay). So it seems like the amount of money a movie makes across the world follows *roughly* an exponential distribution, while there are some outliers that make insane amount of money.\n",
    "\n",
    "**Q: Which is the most successful movie in our dataset?**\n",
    "\n",
    "You can use the following\n",
    "\n",
    "- `idxmax()`: https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.idxmax.html\n",
    "- `loc`: https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.loc.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "Sn-R7A9YCpQc",
    "outputId": "1d581d64-865f-4613-e3be-8c7c3f673349"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Title                                  Avatar\n",
       "US_Gross                          760167650.0\n",
       "Worldwide_Gross                  2767891500.0\n",
       "US_DVD_Sales                      146153933.0\n",
       "Production_Budget                 237000000.0\n",
       "Release_Date                      Dec 18 2009\n",
       "MPAA_Rating                             PG-13\n",
       "Running_Time_min                          NaN\n",
       "Distributor                  20th Century Fox\n",
       "Source                    Original Screenplay\n",
       "Major_Genre                            Action\n",
       "Creative_Type                 Science Fiction\n",
       "Director                        James Cameron\n",
       "Rotten_Tomatoes_Rating                   83.0\n",
       "IMDB_Rating                               8.3\n",
       "IMDB_Votes                           261439.0\n",
       "Name: 1234, dtype: object"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# YOUR SOLUTION HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practical Summary: When to Use Each Technique\n",
    "\n",
    "Ok! After working through this lab, you should now understand when and how to use logarithmic scales and related techniques. Here's a practical guide for real-world applications:\n",
    "\n",
    "### When to Use Log Scale\n",
    "\n",
    "**Use log scale when:**\n",
    "- Comparing ratios: Ratios need symmetric representation (e.g., 10:1 vs 1:10)\n",
    "- Data spans multiple orders of magnitude: Values range from 1 to 1,000,000+\n",
    "- Multiplicative relationships: Growth rates, compound interest, population growth\n",
    "- Visualizing percentage changes: Stock prices, economic indicators\n",
    "- Heavy-tailed distributions: Income, city sizes, word frequencies\n",
    "\n",
    "**Common applications:**\n",
    "- Financial data (stock prices, market caps)\n",
    "- Scientific measurements (earthquake magnitudes, sound intensity)\n",
    "- Web analytics (page views, user engagement)\n",
    "- Biological data (population sizes, gene expression)\n",
    "\n",
    "### When to Use Log-binning\n",
    "\n",
    "**Use log-binning when:**\n",
    "- Creating histograms for heavy-tailed distributions\n",
    "- Linear bins would result in most data falling into the first few bins\n",
    "- You need to see the structure across the entire range of values\n",
    "- The data follows a power law, log-normal, or some heavy-tailed distribution\n",
    "\n",
    "**Key considerations:**\n",
    "- Normalize by bin width (use `density=True`). Otherwise, you may get very misleading results.\n",
    "- Experiment with different numbers of bins to find the right balance\n",
    "- Try both linear and log-scale views for comparison\n",
    "\n",
    "### When to Use CCDF (Complementary CDF)\n",
    "\n",
    "**Use CCDF when:**\n",
    "- Analyzing tail behavior of distributions\n",
    "- Comparing multiple heavy-tailed distributions\n",
    "- Identifying outliers or extreme events\n",
    "\n",
    "**Advantages over regular/log-binned histograms:**\n",
    "- No binning artifacts\n",
    "- Full use of the data\n",
    "- Easier to compare multiple distributions\n",
    "- Clear visualization of rare events\n",
    "\n",
    "### Quick Decision Guide\n",
    "\n",
    "1. **\"My data values vary across many orders of magnitude, like from 10 to 10,000,000\"** → try log-scale and log-binning\n",
    "2. **\"I'm comparing growth rates or ratios\"** → try log-scale\n",
    "3. **\"My histogram has one tall bar and everything else is tiny\"** → try log-binning\n",
    "\n",
    "### Common Pitfalls to Avoid\n",
    "\n",
    "1. **Pay attention to zeros and negative values** in your data\n",
    "2. **Don't forget to normalize histograms** when your bins are not uniform (e.g., log-binning)\n",
    "3. **Always label axes clearly** to indicate log scale usage and binning\n",
    "4. **Consider your audience** - add explanatory notes if they may not be familiar with log scales and binning\n",
    "\n",
    "### Python Quick Reference\n",
    "\n",
    "```python\n",
    "# Log scale for current plot\n",
    "plt.yscale('log')     # using matplotlib.pyplot\n",
    "ax.set_yscale('log')  # using ax object\n",
    "\n",
    "# Log-binning\n",
    "bins = np.logspace(np.log10(data.min()), np.log10(data.max()), n_bins)\n",
    "plt.hist(data, bins=bins, density=True)   # density=True is important! \n",
    "\n",
    "# Quick and dirty CCDF\n",
    "data_sorted = np.sort(data)\n",
    "ccdf = np.linspace(1, 1/len(data), len(data))\n",
    "plt.loglog(data_sorted, ccdf)  # for log-log scale\n",
    "```"
   ]
  }
 ],
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