{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "A6iFUUQLNDlE" }, "source": [ "\n", " \n", " \n", " \n", "
\n", " Run in Google Colab\n", " \n", " View on Github\n", " \n", " View raw on Github\n", "
" ] }, { "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 pandas as pd\n", "import seaborn as sns\n", "import numpy as np\n", "import scipy.stats as ss\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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UVJRycnI817tcLuXn5ysxMVGSlJiYqEOHDqmgoMCzz+rVq+V2u9WxY0cvrAIAAPg6n37LbOjQoerUqZPGjx+v3r17a8OGDZo5c6ZmzpwpSXI4HBoyZIieffZZtWjRQnFxcRo1apRiYmLUo0cPScePKN18880aMGCAsrKyVFlZqfT0dPXp0+c3P2EGAADM49Mfu5ek5cuXa+TIkdq1a5fi4uI0bNgwDRgwwHO9ZVkaM2aMZs6cqUOHDunqq6/WtGnTdPHFF3v2KSkpUXp6upYtWyan06mePXsqMzNT9evXP6UZTudjewAAwDeczuu3zweRLyCIAAA4+5wz30MEAADgDQQRAAAwHkEEAACMRxABAADjEUQAAMB4BBEAADAeQQQAAIxHEAEAAOMRRAAAwHgEEQAAMB5BBAAAjEcQAQAA4/3pILIsS/x+WAAAcDY74yB6/fXX1aZNGwUHBys4OFht27bVG2+8UZOzAQAAeIX/mdxo0qRJGjVqlNLT09W5c2dJ0ieffKKBAwfqhx9+0NChQ2t0SAAAgNrksM7g/a64uDg988wzuv/++6ttnzt3rsaOHavdu3fX2IC+wOVyKSwsTKWlpQoNDbV7HAAAcApO5/X7jN4yO3jwoDp16nTS9k6dOungwYNncpcAAAC2OaMguuiii7Ro0aKTti9cuFAtWrT400MBAAB40xmdQ/TMM8/orrvu0po1azznEK1du1Y5OTm/GUoAAAC+7IyOEPXs2VP5+fk677zztGTJEi1ZskTnnXeeNmzYoNtvv72mZwQAAKhVZ3RStWk4qRoAgLPP6bx+n/JbZi6Xy3NnLpfrd/clGgAAwNnklIOoYcOGOnjwoCIiItSgQQM5HI6T9rEsSw6HQ1VVVTU6JAAAQG065SBavXq1wsPDJUkffvhhrQ0EAADgbaccRNddd53nz3FxcYqNjT3pKJFlWdq/f3/NTQcAAOAFZ/Qps7i4OH3//fcnbS8pKVFcXNyfHgoAAMCbziiITpwr9GtlZWUKCgr600MBAAB402l9MeOwYcMkSQ6HQ6NGjVLdunU911VVVSk/P1+XXXZZjQ4IAABQ204riD777DNJx48QbdmyRQEBAZ7rAgIC1K5dOw0fPrxmJwQAAKhlpxVEJz5d1q9fP02ePJnvGwIAAOeEM/pdZrNnz67pOQAAAGxzRkEkSZs2bdKiRYu0b98+HT16tNp177777p8eDAAAwFvO6FNmCxYsUKdOnbRjxw4tXrxYlZWV2rZtm1avXq2wsLCanhEAAKBWnVEQjR8/Xi+99JKWLVumgIAATZ48WV9++aV69+6tpk2b1vSMAAAAteqMgujrr79W165dJR3/dNmRI0fkcDg0dOhQzZw5s0YHBAAAqG1nFEQNGzbU4cOHJUmNGzfW1q1bJUmHDh3Szz//XHPTAQAAeMEZnVR97bXXKjs7W23atFGvXr00ePBgrV69WtnZ2brhhhtqekYAAIBadUZBNGXKFJWXl0uSnnrqKdWpU0fr1q1Tz549+WJGAABw1jmjt8zCw8MVExNz/A6cTo0YMUKLFi1STEyM2rdvX6MDAgAA1LbTCqKKigqNHDlSCQkJ6tSpk5YsWSLp+Bc1XnjhhZo8ebKGDh1aG3MCAADUmtN6y2z06NGaMWOGkpKStG7dOvXq1Uv9+vXT+vXr9eKLL6pXr17y8/OrrVkBAABqxWkF0dtvv63XX39df/3rX7V161a1bdtWx44d0+effy6Hw1FbMwIAANSq03rL7Ntvv1WHDh0kSa1bt1ZgYKCGDh1KDAEAgLPaaQVRVVWVAgICPD/7+/urfv36NT4UAACAN53WW2aWZalv374KDAyUJJWXl2vgwIGqV69etf345a4AAOBsclpBlJqaWu3ne++9t0aHAQAAsMNpBdHs2bNraw4AAADbnNEXMwIAAJxLCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIAACA8c6qIJowYYIcDoeGDBni2VZeXq60tDQ1atRI9evXV8+ePVVUVFTtdvv27VPXrl1Vt25dRURE6PHHH9exY8e8PD0AAPBVZ00Qbdy4UTNmzFDbtm2rbR86dKiWLVumt99+W7m5uTpw4IDuuOMOz/VVVVXq2rWrjh49qnXr1mnu3LmaM2eORo8e7e0lAAAAH3VWBFFZWZlSUlI0a9YsNWzY0LO9tLRUr776qiZNmqQbbrhBHTp00OzZs7Vu3TqtX79ekvTBBx9o+/btevPNN3XZZZfplltu0bhx4zR16lQdPXrUriUBAAAfclYEUVpamrp27aqkpKRq2wsKClRZWVlte8uWLdW0aVPl5eVJkvLy8tSmTRtFRkZ69klOTpbL5dK2bdt+8/EqKirkcrmqXQAAwLnrtH7bvR0WLFigTz/9VBs3bjzpusLCQgUEBKhBgwbVtkdGRqqwsNCzzy9j6MT1J677LRkZGXrmmWdqYHoAAHA28OkjRPv379fgwYM1b948BQUFee1xR44cqdLSUs9l//79XntsAADgfT4dRAUFBSouLtbll18uf39/+fv7Kzc3V5mZmfL391dkZKSOHj2qQ4cOVbtdUVGRoqKiJElRUVEnfersxM8n9vm1wMBAhYaGVrsAAIBzl08H0Y033qgtW7Zo8+bNnktCQoJSUlI8f65Tp45ycnI8t9m5c6f27dunxMRESVJiYqK2bNmi4uJizz7Z2dkKDQ1VfHy819cEAAB8j0+fQxQSEqLWrVtX21avXj01atTIs71///4aNmyYwsPDFRoaqkcffVSJiYm66qqrJEldunRRfHy87rvvPk2cOFGFhYV6+umnlZaWpsDAQK+vCQAA+B6fDqJT8dJLL8npdKpnz56qqKhQcnKypk2b5rnez89Py5cv16BBg5SYmKh69eopNTVV//jHP2ycGgAA+BKHZVmW3UP4OpfLpbCwMJWWlnI+EQAAZ4nTef326XOIAAAAvIEgAgAAxiOIAACA8QgiAABgPIIIAAAYjyACAADGI4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIAACA8QgiAABgPIIIAAAYjyACAADGI4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIAACA8QgiAABgPIIIAAAYjyACAADGI4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIAACA8QgiAABgPIIIAAAYjyACAADGI4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIAACA8QgiAABgPIIIAAAYjyACAADGI4gAAIDxCCIAAGA8nw6ijIwMXXHFFQoJCVFERIR69OihnTt3VtunvLxcaWlpatSokerXr6+ePXuqqKio2j779u1T165dVbduXUVEROjxxx/XsWPHvLkUAADgw3w6iHJzc5WWlqb169crOztblZWV6tKli44cOeLZZ+jQoVq2bJnefvtt5ebm6sCBA7rjjjs811dVValr1646evSo1q1bp7lz52rOnDkaPXq0HUsCAAA+yGFZlmX3EKfq+++/V0REhHJzc3XttdeqtLRU559/vubPn68777xTkvTll1+qVatWysvL01VXXaUVK1aoW7duOnDggCIjIyVJWVlZevLJJ/X9998rICDgDx/X5XIpLCxMpaWlCg0NrdU1AgCAmnE6r98+fYTo10pLSyVJ4eHhkqSCggJVVlYqKSnJs0/Lli3VtGlT5eXlSZLy8vLUpk0bTwxJUnJyslwul7Zt2/abj1NRUSGXy1XtAgAAzl1nTRC53W4NGTJEnTt3VuvWrSVJhYWFCggIUIMGDartGxkZqcLCQs8+v4yhE9efuO63ZGRkKCwszHOJjY2t4dUAAABfctYEUVpamrZu3aoFCxbU+mONHDlSpaWlnsv+/ftr/TEBAIB9/O0e4FSkp6dr+fLlWrNmjZo0aeLZHhUVpaNHj+rQoUPVjhIVFRUpKirKs8+GDRuq3d+JT6Gd2OfXAgMDFRgYWMOrAAAAvsqnjxBZlqX09HQtXrxYq1evVlxcXLXrO3TooDp16ignJ8ezbefOndq3b58SExMlSYmJidqyZYuKi4s9+2RnZys0NFTx8fHeWQgAAPBpPn2EKC0tTfPnz9fSpUsVEhLiOecnLCxMwcHBCgsLU//+/TVs2DCFh4crNDRUjz76qBITE3XVVVdJkrp06aL4+Hjdd999mjhxogoLC/X0008rLS2No0AAAECSj3/s3uFw/Ob22bNnq2/fvpKOfzHjY489prfeeksVFRVKTk7WtGnTqr0dtnfvXg0aNEgfffSR6tWrp9TUVE2YMEH+/qfWg3zsHgCAs8/pvH77dBD5CoIIAICzzzn7PUQAAAC1gSACAADGI4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIAACA8QgiAABgPIIIAAAYjyACAADGI4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCABgq/LKKn1/uELllVV2jwKD+ds9AADATBv3lOiVj79R9vYiuS3J6ZBuio/UgGsuUELzcLvHg2E4QgQA8Lo31u9V76w8rdpRLLd1fJvbklbtKFavrDy9uX6vvQPCOAQRAMCrNu4p0eglW2VJqjpRQ/+nym3JkjRqyVZt2lNiy3wwE0EEAPCqVz7+Rk6n43f3cTodeuWT3V6aCCCIAABeVF5ZpeztRScdGfq1KrelD7YVcqI1vIYgAgB4zeHyY/qDFvJwW8f3B7yBIAIAeE1IkL/+4N0yD6fj+P6ANxBEAACvCarjp5viI+X3B1Xk53Soy6VRCqrj56XJYDqCCADgVQ9ec4Hcf/C+mdtt6cGr47w0EUAQAQC87Irm4RrXo7Uc0klHivycDjkkjevRmi9nhFfx5iwAwOvuvaqZWkaF6JVPduuDbYXVvqn6wavjiCF4HUEEALBFQvNwJTQPV3lllQ6XH1NIkD/nDME2BBEAwFZBdfwIIdiOc4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIAACA8QgiAABgPIIIAAAYjyACAADGI4gAAIDxCCIAAGA8gggAABiPIAIAAMYjiAAAgPEIIgCwWXlllb4/XKHyyiq7RwGM5W/3AABgqo17SvTKx98oe3uR3JbkdEg3xUdqwDUXKKF5uN3jAUbhCBEA2OCN9XvVOytPq3YUy20d3+a2pFU7itUrK09vrt9r74CAYQgim5l+qNz09Us8Byauf+OeEo1eslWWpKoTNfR/qtyWLEmjlmzVpj0ltswHmIi3zGxi+qFy09cv8RyYvP5XPv5GTqfjpBj6JafToVc+2X3OPxeArzDqCNHUqVPVvHlzBQUFqWPHjtqwYYMtc5h+qNz09Us8Byavv7yyStnbi343hqTjR4o+2FZo1JEzwE7GBNHChQs1bNgwjRkzRp9++qnatWun5ORkFRcXe3UO0w+Vm75+iefA9PUfLj+mP2ghD7d1fH8Atc+YIJo0aZIGDBigfv36KT4+XllZWapbt65ee+01r85x4lD57zlxqPxcZPr6JZ4D09cfEuSvP1i+h9NxfH8Atc+IIDp69KgKCgqUlJTk2eZ0OpWUlKS8vLyT9q+oqJDL5ap2qQmmHyo3ff0Sz4Hp65ekoDp+uik+Un5/UEV+Toe6XBqloDp+XpoMMJsR//T44YcfVFVVpcjIyGrbIyMj9eWXX560f0ZGhp555pkan+O/HSo/sj1XR3bkSpLO6zZch9a8rmOuYo2ozNUTw4Zo4MCBkqQBAwaosrJSc+bMkSS99tprev7557Vz505ddNFFevrpp9W3b19J0n333ae6detqxowZkqRp06ZpxowZ+vzzzxUbG6sXXnhBffr0kST17t1b0dHRmjx5siTppZde0ltvvaUNGzYoIiJCM2bM0O233y5Juu2223TJJZdo4sSJkqQJEybof/7nf/Txxx8rNDRUb775pu644w4dO3ZMycnJuvLKKzVu3DhJ0uDH/65Dm5apfM9ncvjV0fk9Rur7916QVfm/CoptraC4y3VozeuSpNCOvTR1+h7lrnpfkvTee++pX79++vHHH5WYmKg777xTjz32mCRp2LBh2rdvn9555x1J0qJFizR06FB99913at++vfr376/09HRJ0iOPPKLS0lLNmzdPkvTGG29ozJgx+uabb9SqVSsNGzZMAwYMkCQ98MADnudZkmbNmqVJkyZpx44duuCCC/TMM8/ovvvukySlpKQoLCxM06ZNkyRNmTJFr776qj777DM1btxYL730knr37q2jx9xyOS+Wf+j5cm1cIklqeH1//bxzrSoOfClnUKjO6zpExf/+hyRpavQeJSa014QJEyRJzz33nD744APl5uaqfv36mj9/vnr16qWKigrddNNN6ty5s8aOHStJGjVqlDZs2KD3339f/v7+evfdd3XvvffK5XLpmmuuUdeuXTVixAhJ0hNPPKGdO3dq6dKlkqTFixfr4YcfVnFxsa688krdfffdGjp06PH/joMH6+DBg1q0aJEkacGCBXr88ce1f/9+tWvXTg8//LAeeeQRSdLDDz+sn3/+WW+88YYk6Z8vz9APq2bp2KGDqhPeRKEde+rHFcf/d1e/dZLk56eyz4//Nw/vkqYRI0fqm6++VLNmzTR+/HilpKRIku6++241atRIU6ZMkSRlZmbq9ddf16ZNmxQdHa0pU6aoZ8+ekqTbb79dF154of75z39KkiZOnKilS5dq7dq1atiwoebOnasePXrI7Xbr1ltvVfv27fXcc89Jkv7xj3/oo48+0urVqxUcHKyFCxfqrrvu0v/+7//qhhtu0F/+8heNHj1akvTUU0/ps88+0//7f/9PTqdTS5YsUWpqqn766Sd17txZt912m5544glJUteUh/Tvzav0867j/yA7v8ffVZKdpaojJQqIaqH6rW9Q8aoZ2t4sXB9EDNWPP/6ot956S5I0b948/f3vf9fevXvVunVrpaennzN/R4wdO1Zr165Vdna2AgMD9fbbb+uee+5RWVmZrrvuOnXp0kVPPfWUJGnEiBHaunWrli9ffk79HSFJd955p5o2bapJkyZJkl588UW98847ysvLU6NGjTR79mz99a9/lSR169ZNrVu3Pif+jrj77rt19913yy4Oy7JO8d3ss9eBAwfUuHFjrVu3TomJiZ7tTzzxhHJzc5Wfn19t/4qKClVUVHh+drlcio2NVWlpqUJDQ894jvLKKsWPXnlK5w84HdL2f9x8Tv3r0PT1SzwHpq//l95cv1ejlmw96dNmfk6H3G5L43q01r1XNbNxQuDs53K5FBYWdkqv30a8ZXbeeefJz89PRUVF1bYXFRUpKirqpP0DAwMVGhpa7VITTD9Ubvr6JZ4D09f/S/de1UxvD0zUTfGRnnOKTnz1wNsDE4khwMuMeMssICBAHTp0UE5Ojnr06CFJcrvdysnJ8Rwm9ZYHr7lAH2wr+t193G5LD14d56WJvMv09Us8B6av/5cSmocroXm4yiurdLj8mEKC/M/pCAR8mRFHiKTj7yHPmjVLc+fO1Y4dOzRo0CAdOXJE/fr18+ocVzQP17gereWQTvpXsp/TIYekcT1an7Nfxmb6+iWeA9PX/1uC6vjp/JBAYgiwkRHnEJ0wZcoUvfDCCyosLNRll12mzMxMdezY8Q9vdzrvQZ6qTXtK9Monu/XBtkLPt/R2uTRKD14dZ8QLgenrl3gOTF8/gNp3Oq/fRgXRmaqNIDrB9EPlpq9f4jkwff0Aas/pvH4bcQ6RLwuq42f0i4Dp65d4DkxfPwDfYMw5RAAAAP8NQQQAAIxHEAEAAOMRRAAAwHgEEQAAMB5BBAAAjEcQAQAA4xFEAADAeHwx4yk48WXeLpfL5kkAAMCpOvG6fSq/lIMgOgWHDx+WJMXGxto8CQAAOF2HDx9WWFjY7+7D7zI7BW63WwcOHFBISIgcDscf3+A0uFwuxcbGav/+/TX+e9LOBqavX+I5MH39Es8B6zd7/VLtPQeWZenw4cOKiYmR0/n7ZwlxhOgUOJ1ONWnSpFYfIzQ01Nj/I0isX+I5MH39Es8B6zd7/VLtPAd/dGToBE6qBgAAxiOIAACA8QgimwUGBmrMmDEKDAy0exRbmL5+iefA9PVLPAes3+z1S77xHHBSNQAAMB5HiAAAgPEIIgAAYDyCCAAAGI8gAgAAxiOIbDR16lQ1b95cQUFB6tixozZs2GD3SF6zZs0ade/eXTExMXI4HFqyZIndI3lVRkaGrrjiCoWEhCgiIkI9evTQzp077R7Lq6ZPn662bdt6vogtMTFRK1assHss20yYMEEOh0NDhgyxexSvGTt2rBwOR7VLy5Yt7R7Lq7777jvde++9atSokYKDg9WmTRtt2rTJ7rG8pnnz5if9b8DhcCgtLc3rsxBENlm4cKGGDRumMWPG6NNPP1W7du2UnJys4uJiu0fziiNHjqhdu3aaOnWq3aPYIjc3V2lpaVq/fr2ys7NVWVmpLl266MiRI3aP5jVNmjTRhAkTVFBQoE2bNumGG27Qbbfdpm3bttk9mtdt3LhRM2bMUNu2be0exesuvfRSHTx40HP55JNP7B7Ja3766Sd17txZderU0YoVK7R9+3a9+OKLatiwod2jec3GjRur/ffPzs6WJPXq1cv7w1iwxZVXXmmlpaV5fq6qqrJiYmKsjIwMG6eyhyRr8eLFdo9hq+LiYkuSlZuba/cotmrYsKH1yiuv2D2GVx0+fNhq0aKFlZ2dbV133XXW4MGD7R7Ja8aMGWO1a9fO7jFs8+STT1pXX3213WP4lMGDB1sXXnih5Xa7vf7YHCGywdGjR1VQUKCkpCTPNqfTqaSkJOXl5dk4GexSWloqSQoPD7d5EntUVVVpwYIFOnLkiBITE+0ex6vS0tLUtWvXan8fmGTXrl2KiYnRBRdcoJSUFO3bt8/ukbzmvffeU0JCgnr16qWIiAi1b99es2bNsnss2xw9elRvvvmmHnjggRr/ReqngiCywQ8//KCqqipFRkZW2x4ZGanCwkKbpoJd3G63hgwZos6dO6t169Z2j+NVW7ZsUf369RUYGKiBAwdq8eLFio+Pt3ssr1mwYIE+/fRTZWRk2D2KLTp27Kg5c+Zo5cqVmj59unbv3q1rrrlGhw8ftns0r/jmm280ffp0tWjRQu+//74GDRqkv/3tb5o7d67do9liyZIlOnTokPr27WvL4/Pb7gGbpaWlaevWrUadO3HCJZdcos2bN6u0tFTvvPOOUlNTlZuba0QU7d+/X4MHD1Z2draCgoLsHscWt9xyi+fPbdu2VceOHdWsWTMtWrRI/fv3t3Ey73C73UpISND48eMlSe3bt9fWrVuVlZWl1NRUm6fzvldffVW33HKLYmJibHl8jhDZ4LzzzpOfn5+KioqqbS8qKlJUVJRNU8EO6enpWr58uT788EM1adLE7nG8LiAgQBdddJE6dOigjIwMtWvXTpMnT7Z7LK8oKChQcXGxLr/8cvn7+8vf31+5ubnKzMyUv7+/qqqq7B7R6xo0aKCLL75Y//nPf+wexSuio6NPiv9WrVoZ9bbhCXv37tWqVav04IMP2jYDQWSDgIAAdejQQTk5OZ5tbrdbOTk5xp0/YSrLspSenq7Fixdr9erViouLs3skn+B2u1VRUWH3GF5x4403asuWLdq8ebPnkpCQoJSUFG3evFl+fn52j+h1ZWVl+vrrrxUdHW33KF7RuXPnk75u46uvvlKzZs1smsg+s2fPVkREhLp27WrbDLxlZpNhw4YpNTVVCQkJuvLKK/Wvf/1LR44cUb9+/ewezSvKysqq/Stw9+7d2rx5s8LDw9W0aVMbJ/OOtLQ0zZ8/X0uXLlVISIj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" ] }, "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": [ "
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TitleUS_GrossWorldwide_GrossUS_DVD_SalesProduction_BudgetRelease_DateMPAA_RatingRunning_Time_minDistributorSourceMajor_GenreCreative_TypeDirectorRotten_Tomatoes_RatingIMDB_RatingIMDB_Votes
4Slam1009819.01087521.0NaN1000000.0Oct 09 1998RNaNTrimarkOriginal ScreenplayDramaContemporary FictionNone62.03.4165.0
8Pirates1641825.06341825.0NaN40000000.0Jul 01 1986RNaNNoneNoneNoneNoneRoman Polanski25.05.83275.0
9Duel in the Sun20400000.020400000.0NaN6000000.0Dec 31 2046NoneNaNNoneNoneNoneNoneNone86.07.02906.0
10Tom Jones37600000.037600000.0NaN1000000.0Oct 07 1963NoneNaNNoneNoneNoneNoneNone81.07.04035.0
11Oliver!37402877.037402877.0NaN10000000.0Dec 11 1968NoneNaNSony PicturesNoneMusicalNoneNone84.07.59111.0
\n", "
" ], "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": { "image/png": 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"text/plain": [ "
" ] }, "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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", "text/plain": [ "
" ] }, "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": [ "
" ] }, "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": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": [ "
" ] }, "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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": { "id": "UXbtx84FCpQa" }, "source": [ "**Q: Can you explain the plot? Why are there gaps?**" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "id": "Flb3oWYCCpQa" }, "outputs": [], "source": [ "# YOUR SOLUTION HERE" ] }, { "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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", 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" ] }, "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": [ "
" ] }, "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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eXg61Wg0vLy+d5V5eXiguLu72+8TFxeGBBx7ADz/8AD8/vy5LlK2tLZydnXUelkqSJLx4dwjcHWxQe60Fmw7myR2JiIhIr2Q/NdYXfvrpJ7kjmCwrpQK/mzgYb+7Kwdu7z2CsnytihnrIHYuIiEgvjPqIUP/+/aFUKlFSonvlUklJCby9vWVKZXmWTBqCicP6o6lFg8c2puJKHSdaJCIi82DURcjGxgYRERFITEzULtNoNEhMTERMTIxBt61SqRASEoLIyEiDbscU2Fgp8K9HIuDtbIeGZjUe+OgQKuub5I5FRETUa7IXobq6OmRkZGiv/MrNzUVGRgby8/MBAAkJCVi3bh02bdqE06dP4w9/+APq6+u1V5EZSnx8PLKyspCammrQ7ZgKexsrqB4eB1d7a1woq8eL35yUOxIREVGvyT5GKC0tDbGxsdrnCQkJAIBFixZh48aNmD9/PsrKyvDSSy+huLgYYWFh2LlzZ7sB1GR4EYPc8M78MCzekIrknDKoNQJKhSR3LCIiopsmCSGE3CGMWU1NDVxcXFBdXW3RV5Bd16LWYOwrP+Jqkxor7gzG7ycNgZVS9gOLREREOrr7+5u/wahHrJQKPBQVAAD4x84cLPjkCNiliYjIVLEIdYKDpTu3csYIPHX7cADA4QsVOF9WL3MiIiKim8NTYzfAU2OdW/DxEew/V44Zo73xz4fHQZI4XoiIiIwDT42RwS27bRgAYMfJYnyVfknmNERERD3HIkQ37ZYhHlg8IRAA8JetJ5F/5aq8gYiIiHqIRYh65U93jkCAuz2a1Bp8lW6ZN6glIiLTxSJEvWJnrcSzdwQBAFRJ55BVWCNzIiIiou5jEeoErxrrvpljfBDi4wyNAO5fexCFVQ1yRyIiIuoWXjV2A7xqrHtyimvx4L8OofJqM2aF+uL9h8LljkRERBaMV41Rnwr2dsK/H4+GQgK+O16IIxeuyB2JiIjohliESG9G+bpoZ51+9YfTnHGaiIiMHosQ6dXyuCDYKBU4caka358okjsOERFRl1iESK8GONnisYmDAQAJX2bg5OVqmRMRERF1rttFaPLkyaiqqtI+//bbb9HQYL5XB/GqsZu3PG44YoZ4oFkt8OI3J+WOQ0RE1KluXzWmUChQXFwMT09PAICzszMyMjIwZMgQgwaUG68auzlnSmpxxzt7AQCJz07B0AGOMiciIiJLYvCrxjgQlroS5OWEqEB3AMDbP+bw54WIiIwSxwiRwTwxpfVo4Q+ZxUjJrZA5DRERUXtWPVl5165dcHFxAQBoNBokJibi5EndMSCzZ8/WXzoyabeP9MKEYR44cO4KtmUUInqIh9yRiIiIdPSoCC1atEjn+RNPPKHzXJIkqNXq3qcis7EoJhAHzl3BkVxOsEhERMan20VIo9EYMgeZqci2cUIXyupRUd8EdwcbmRMRERH9gmOEyKDcHGwwdIADACA1j+OEiIjIuPTo1BgA/Pzzz9iyZQvy8vIgSRIGDx6M+++/H5MnTzZEPtmoVCqoVCqe6tODqMEeOF9Wjy1HL2H6KG+54xAREWn16O7zS5cuxb/+9S+4ubkhKCgIQgicPXsWVVVV+OMf/4j333/fkFllwXmEei8ltwLzPjoEK4WEI3++HR6OtnJHIiIiM6f3eYS2bt2KDRs2YP369SgvL8ehQ4dw+PBhlJWVYd26dfjXv/6Fb7/9Vi/hybxEBroh0MMeLRqBZ748zjmFiIjIaHS7CG3YsAEJCQl49NFHIUnSL2+gUOCxxx7D8uXL8cknnxgkJJk2SZKwPC4IALD3TBnmf3QYDU085UhERPLrdhE6evQo7rnnnk5fv/fee5Genq6XUGR+5oYPxF9mjgQApORVYHNqvsyJiIiIelCEysvL4efn1+nrfn5+uHKFc8VQ5x6fNAQJ01qPDH28PxdXm1pkTkRERJau20WoqakJ1tbWnb5uZWWFpqYmvYQi8zU/0h82VgpcqmzA019kyB2HiIgsXI8un3/xxRdhb2/f4WtXr17VSyAyb17OdkiYFoTXd2Rjd1YJth67hHvCOz/SSEREZEjdLkKTJ09GTk7ODdchupHFEwKx42QxjhdU4c9bTiJqsAcGuvaTOxYREVmgHs0jZIk4j5Bh1De2YMqbSSiva4K/ez98/vgt8Hfv+GgjERFRT+l9HqHrb9rRPcc0Gg1qamp6ntKIqVQqhISEIDIyUu4oZsnB1gqbHouCk60VCioa8MDaQ6io5xgzIiLqWz2aUHH8+PG4du1au9caGhoQGRmJ7777Tq/h5BQfH4+srCykpqbKHcVsjfJ1wXdPTsQgD3sU11zDiv8elzsSERFZmG4XoQ8//BArVqzocLC0g4MD/vSnP+GDDz7Qazgyf4H9HfDGfWMBAD+dLsVHe85z5mkiIuoz3S5CJ0+exNSpUzt9ffLkycjMzNRHJrIwtwzxwKKYQQCA19quJiMiIuoL3S5ClZWVaGnpfAK85uZmVFZW6iUUWZ6XZ49CZKAbAODZL48jJbdC5kRERGQJul2EAgMDkZaW1unraWlpGDRokF5CkeWRJAkfLohAsJcTahtbMO+jQ/jg57NyxyIiIjPX7SJ077334oUXXkBJSfvTFsXFxfjLX/6C++67T6/hyLL0d7TFZ0uiMXpg62WOb/14Bq9uz+KYISIiMphuzyNUW1uLmJgY5OfnY8GCBQgODgYAZGdn47PPPoO/vz8OHz4MJycngwbua5xHqO8JIbDivyfwVfolAMCGxZGIDfaUORUREZmS7v7+7tGEitXV1Vi1ahU2b96sHQ/k6uqKBx98EK+++irc3Nx6n9zIsAjJ50//PYHNaQVwtrPClj9OwDBPR7kjERGRiTBIEbpOCIHy8nIIITBgwABIktSrsMaMRUg+xdXXMFd1AMU11/C7iYPx4t0hckciIiITYZCZpa+TJAkDBgyAp6enWZcgkpe3ix1WzhgBAPjpdAnHChERkd7dVBEi6it3jPKCjZUCF69cxemiWrnjEBGRmWERIqNmb2OF20e0DpT+POWizGmIiMjcsAh1gjddNR4Lbmmdn+qzI/lQJZ2TOQ0REZmTmxosbUk4WFp+Qgi88l0WNh7MAwB8viQatw7tL28oIiIyat39/W3VnTd77733ur3hp556qtvrEnWHJEl4efYoFFRcRWJ2KbYdu4yYIR4cqE9ERL3WrSNCgwcP7t6bSRIuXLjQ61DGhEeEjEdSdikWb0wFAKycMQJLpwyVORERERkrg84jZElYhIyLKukc3tyVAxsrBY69OA0Ott06qElERBbGoPMIEcnlj1OHwtnOCk0tGuRXXJU7DhERmbib+nP60qVL+Pbbb5Gfn4+mpiad19asWaOXYEQdkSQJ/u72OFVYgz1nyjDSh0fpiIjo5vW4CCUmJmL27NkYMmQIsrOzMXr0aOTl5UEIgXHjxhkiI5GOuJFeOFVYg9d3ZMO1nzUejAqQOxIREZmoHp8aW7VqFZ577jlkZmbCzs4OX3/9NQoKCjBlyhQ88MADhshIpOPp24djyaTWAfwrt2Ri/f5c5JbX8xYcRETUYz0eLO3k5ISMjAwMHToUbm5u2L9/P0aNGoXjx49jzpw5yMvLM1BUeXCwtHESQmDKm8k644SGDHDA54/fAm8XOxmTERGRMTDYYGkHBwftuCAfHx+cP39e+1p5eflNRCXqOUmS8OnvovBMXBCiBrvDWinhQlk9DpzjzyAREXVfj4vQLbfcgv379wMA7rrrLjz77LN49dVX8dhjj+GWW27Re0CizgzycMDTccPx5RMxmBXqCwC4XNUgcyoiIjIlPR4svWbNGtTV1QEAXnnlFdTV1WHz5s0YPnw4rxgj2fi59gMAvJd4FiN9nDEtxEvmREREZAo4oeINcIyQaSipuYb7PjyIS5UNUEjAuVfvgkLBW3AQEVkqg40RSk1NxZEjR9otP3LkCNLS0nr6dkR64eVshx+engQA0AjwLvVERNQtPS5C8fHxKCgoaLf88uXLiI+P10soopvhbGeNhGlBAIC3d59Bac01mRMREZGx63ERysrK6nDixPDwcGRlZeklFNHNWhQTiOtnxCb9Iwn/TD7H+YWIiKhTPS5Ctra2KCkpabe8qKgIVlbmcwNMlUqFkJAQREZGyh2FesDF3hpf/D4G4wJc0diiwT925mDN7jNyxyIiIiPV48HSDz30EIqKivDNN9/AxcUFAFBVVYW5c+fC09MTX375pUGCyoWDpU2TEAIbD+bhle9aj1L+fvIQzBjtjVA/Vw6iJiKyAN39/d3jInT58mVMnjwZV65cQXh4OAAgIyMDXl5e2L17N/z9/XuX3MiwCJm2F7Zm4rMj+drn3s52WHXXCMwJGyhjKiIiMjSDFSEAqK+vx2effYbjx4+jX79+GDt2LB566CFYW1v3KrQxYhEybWqNwI6TRdh5shjfnygCAAx07Yc9z0+FlbLHZ4aJiMhEGLQIWRIWIfNRfbUZYX/9EUIA90f44a0HQuWOREREBtLd39/dGt387bffYsaMGbC2tsa3337b5bqzZ8/uWVKiPuJib41/LRyPpf9Ox3/TL2FRTCDG+LnIHYuIiGTUrSI0d+5cFBcXw9PTE3Pnzu10PUmSoFar9ZWNSO+mhXhhxmhvfH+iCF+lF7AIERFZuG4NktBoNPD09NT+d2cPliAyBfPGtw7o//xIPv6Tkn+DtYmIyJz1aLRoc3Mzbr/9dpw9e9ZQeYgMbuKw/rgnfCBaNAKrtmRiz5kyuSMREZFMelSErK2tceLECUNlIeoTCoWENfNCMb/tyNAr357C0fxKmVMREZEcenz98IIFC/DJJ58YIgtRn5EkCcunDYeHgw0ulNfj3n8exP9+lwW1hhdREhFZkh7fE6OlpQXr16/HTz/9hIiICDg4OOi8vmbNGr2FIzIkH5d++PGZyXh9Rza+Sr+E9QdyUVTdANX/jOPs00REFqLHRejkyZPam66eOaN7DydJ4i8PMi0ejrZ484FQTA32xDObM7DjZDH2nC1DbLCn3NGIiKgP9LgIJSUlGSIHkaxmjvXBnjOl+DLtEo5cqGARIiKyELzHAFGbyEB3AEByTimaWjQypyEior7QrSNC9957LzZu3AhnZ2fce++9Xa67ZcsWvQQj6muTgwbAzlqB7OJa/G5TKhbeMghhAa7wdLKTOxoRERlIt4qQi4uLdvyPiwtn4iXz5OVsh48ficTvNqVi39ly7DtbDgDwc+uH8AA3hPu7YtwgN4wd6MLB1EREZoI3Xb0B3nTV8py4VIXPDucjo6AKZ0pr8dt/IdNCvPDRggiWISIiI2bwu8+XlpYiJycHABAcHKy9BYe5YRGybLXXmnHiUjWO5VfiWH4V9p0rR1OLBv8THYBHbw3EcE9HXi1JRGSEDFaEampqEB8fjy+++EJ7bzGlUon58+dDpVKZ3akzFiH6tf+k5GPVlkzt8yEDHDBjtDdmjPbBKF9nliIiIiPR3d/fPb5qbMmSJThy5Ai+//57VFVVoaqqCt9//z3S0tLwxBNP9Co0kbF7MNIfqv8Zh9tGeMJGqcCFsnqoks7j7vf34+739+PL1AJca+bNh4mITEWPjwg5ODhg165dmDhxos7yffv24c4770R9fb1eA8qNR4SoMzXXmpGUXYodmcVIyilFY9sl96721ng4OgBP3x4EGyvOUEFEJIfu/v7u8YSKHh4eHZ7+cnFxgZubW0/fjshkOdtZY07YQMwJG4jK+iZ8mVaATw9fxKXKBqiSzuNaswYv3h0id0wiIupCj/9c/ctf/oKEhAQUFxdrlxUXF+P555/Hiy++qNdwRKbCzcEGT0wZij3Px+If940FAHyyPxcbD+SCF2YSERmvHp8aCw8Px7lz59DY2IiAgAAAQH5+PmxtbTF8+HCddY8ePaq/pDLhqTG6GS9/ewobD+YBaJ2o8R/3jYW3CydmJCLqKwY7NTZ37tze5OpzBQUFWLhwIUpLS2FlZYUXX3wRDzzwgNyxyMy9dHcIAtzt8cbObOw9U4aH1h3GTwlToOTcQ0RERsXsJ1QsKipCSUkJwsLCUFxcjIiICJw5cwYODg7d+noeEaLeOFdah3v+eQC111rw36UxGN92PzMiIjIsg10+/2t1dXWoqanReRgbHx8fhIWFAQC8vb3Rv39/VFRUyBuKLMYwT0fcPqJ1stE1u8+gWc2buRIRGZMeF6Hc3FzMnDkTDg4O2ivF3Nzc4OrqelNXje3duxezZs2Cr68vJEnCtm3b2q2jUqkQGBgIOzs7REdHIyUlpcfbAYD09HSo1Wr4+/vf1NcT3Yw/xg6Dg40SB89fwV+2nkQLyxARkdHo8RihBQsWQAiB9evXw8vLq9cz6dbX1yM0NBSPPfZYh3e237x5MxISErB27VpER0fj3XffxfTp05GTk6O9rUdYWBhaWlrafe2PP/4IX19fAEBFRQUeeeQRrFu3rss8jY2NaGxs1D43xqNcZFqCvJzw/x4Mx5JP07A5rQBnS2vxzvwwDPLo3ulZIiIynB6PEXJ0dER6ejqCg4P1H0aSsHXrVp0B2dHR0YiMjMQHH3wAANBoNPD398eTTz6JlStXdut9GxsbMW3aNCxZsgQLFy7sct2XX34Zr7zySrvlHCNEvfXd8UL8eUsmahtb4GCjxFsPhGLGGB+5YxERmSWDjRGKjIxEQUFBr8J1V1NTE9LT0xEXF6ddplAoEBcXh0OHDnXrPYQQePTRR3HbbbfdsAQBwKpVq1BdXa199NX3SuZvVqgvdiyfhKhAd9Q3qfHOT2fkjkREZPF6fGrs448/xtKlS3H58mWMHj0a1tbWOq+PHTtWb+HKy8uhVqvh5eWls9zLywvZ2dndeo8DBw5g8+bNGDt2rHb80aeffooxY8Z0uL6trS1sbW17lZuoM35u9lhxZzDuX3sITS0cK0REJLceF6GysjKcP38eixcv1i6TJAlCCEiSpL0jvbGYOHEiNBr+wiHjYWulBADUXmvR/rshIiJ59LgIPfbYYwgPD8d//vMfvQyW7kr//v2hVCpRUlKis7ykpATe3t4G2y6RIQ3zdIRSIeFKfROKa67Bx6Wf3JGIiCxWj8cIXbx4EW+88Qaio6MRGBiIQYMG6Tz0ycbGBhEREUhMTNQu02g0SExMRExMjF639VsqlQohISGIjIw06HbI8vSzUWKEtxMA4Ov0SzKnISKybD0uQrfddhuOHz+utwB1dXXIyMhARkYGgNZ5ijIyMpCfnw8ASEhIwLp167Bp0yacPn0af/jDH1BfX69zas4Q4uPjkZWVhdTUVINuhyzT45MGAwDeSzyHc6W1MqchIrJcPT41NmvWLDzzzDPIzMzEmDFj2g2Wnj17do/eLy0tDbGxsdrnCQkJAIBFixZh48aNmD9/PsrKyvDSSy+huLgYYWFh2LlzZ7sB1ESmZG7YQHybUYiknDL8/YdsrH+URx6JiOTQ43mEFIrODyIZ42Dp3uK9xshQsgprcNd7+9DPWokTL98Ba2Wv7nhDRES/YrB5hDQaTacPcytBRIY0wtsJLv2s0dCsRnJOmdxxiIgsEv8E7QQHS5OhKRQS4ka2nuL942fp2JyaL3MiIiLL0+0idNddd6G6ulr7/PXXX0dVVZX2+ZUrVxASEqLXcHLiYGnqC3+bOxozx/igWS3wp68z8dfvs9DDs9VERNQL3S5Cu3bt0rkZ6d///ndUVFRon7e0tCAnJ0e/6YjMXD8bJT74n3A8ExcEAPhkfy5+zCq5wVcREZG+dLsI/favVP7VSqQfkiTh6bjheCSmdR6u5JxSmRMREVkOjhEiMhKxwZ4AgL1nyqHW8A8NIqK+0O0iJElSu9tp8B5JRPoTNdgdDjZKXK5qwKvbT8sdh4jIInR7QkUhBB599FHtndmvXbuGpUuXwsHBAQB0xg+ZA5VKBZVKxSkBqM842FrhH/eHIv7zo1h/IBdDBjhgwS36vW0NERHp6vaEit29pcWGDRt6FcjYcEJF6msf/HwWb/14BkqFhGfihuPxSUNgZ62UOxYRkUnp7u/vHs8sbWlYhKivCSGw4r8n8FXbDVkD3O3xwsyRuCPEi6ejiYi6yWAzSxORYUmShH/cPxbvzg+Dl7Mt8iuu4olP0/HI+hTeoJWISM9YhIiMkCRJmBs+ED8/OxXxsUNho1Rg39lyTH93H7afKJI7HhGR2WARIjJiDrZWeH76COxOmIzY4AFQawRe/u4U6htb5I5GRGQWWISITMAgDwd8tHA8BnnYo6y2ER/tvSB3JCIis8Ai1AnedJWMjY2VAn+6cwQA4F97z6O4+prMiYiITB+LUCd401UyRjNGe2P8IDdca9bgrR95bz8iot5iESIyIZIk4YWZIwEAXx+9hFOF1TInIiIybSxCRCYmPMANs0J9IQTw6vbTvAEyEVEvsAgRmaAV04NhY6XAwfNXkHaxUu44REQmi0WIyAT5u9tj+ihvAMDh81dkTkNEZLpYhIhM1LgAVwDA0XweESIiulksQp3g5fNk7MYFuAEAjhVUcZwQEdFNYhHqBC+fJ2M30scZdtYKVF1t5gSLREQ3iUWIyETZWCnw3B3BAIDXd2Tj8yP5MiciIjI9LEJEJuzxSUPwx6lDAQAvbMvEt8cLZU5ERGRaWISITNzz04Ox4JYACAEkbM5AUnap3JGIiEwGixCRiZMkCf87ezRmh/qiRSOwfHMGWtQauWMREZkEFiEiM6BQSHh7XiislRKqG5pRUtsodyQiIpPAIkRkJqyVCni72AEACqsaZE5DRGQaWISIzIivSz8ALEJERN3FIkRkRnxdrxehazInISIyDSxCneDM0mSKBvd3AADsOcMrx4iIuoNFqBOcWZpM0X0RfrBSSDh8oQInLlXJHYeIyOixCBGZkYGu/TAr1BcAeNsNIqJuYBEiMjO/nzwEALAjswj5V67KnIaIyLixCBGZmZE+zpgcNAAaAXy8n0eFiIi6wiJEZIYWTwgEAOzOKpE3CBGRkWMRIjJD/m6tl9FfbVLLnISIyLixCBGZIRulEgDQ1MJ7jhERdYVFiMgM2Vi1/tNu4s1XiYi6xCJEZIauFyG1RkCtETKnISIyXixCRGboehECeHqMiKgrLEJEZqiftRJOdlYAgN2neeUYEVFnWISIzJBSIeH3k1onVnxzVzYaW3j1GBFRR1iEOsGbrpKp+92kwfB0skVBRQP+fThf7jhEREZJEkJwJGUXampq4OLigurqajg7O8sdh6hHvkjJx8otmXC1t8ae52Ph0s9a7khERH2iu7+/eUSIyIzdH+GH4Z6OqLrajA+Tz8sdh4jI6LAIEZkxK6UCK2eMAACsP5CLy1UNMiciIjIuLEJEZu62EZ6IHuyOphYNEjZnoLK+Se5IRERGg0WIyMxJkoQX7w5BP2sljuRWYNYH+3GqsFruWERERoFFiMgCjB7ogi1/vBUB7va4VNmA+z48iG3HLssdi4hIdixCRBZipI8zvl02AVOCBuBaswbLN2fgle9OoZn3IyMiC8YiRGRBXO1tsP7RSCyLHQYA2HAgDws+PoKy2kaZkxERyYNFiMjCKBUSnpsejLULIuBoa9U6buj9/cgoqJI7GhFRn2MRIrJQd472xrb4WzFkgAOKa65h3tpD2JzKGaiJyLKwCBFZsGGeTvgmfgKmhXihSa3Bn77OxJ+3ZvLeZERkMViEiCyck501PloQgWenBUGSgM+P5GPN7jNyxyIi6hMsQkQEhULCk7cPx6q2WaizCmtkTkRE1DdYhIhIy8elHwCgRc17MRORZWARIiItK4UEAFBrWISIyDKwCBGRlrKtCLVoOMkiEVkGFqFOqFQqhISEIDIyUu4oRH3GSskjQkRkWViEOhEfH4+srCykpqbKHYWoz1gpWj8SmjlGiIgsBIsQEWlxjBARWRoWISLS4hghIrI0LEJEpMUxQkRkaViEiEjLRqkEANRca4EQLENEZP5YhIhIa7iXI+xtlKiob8Ipzi5NRBaARYiItOyslZg4rD8AIPF0qcxpiIgMj0WIiHTcPtITAPBzdonMSYiIDI9FiIh0xI5oLULHL1WjtOaazGmIiAyLRYiIdHg62SHU3xUA8HM2T48RkXljESKiduLajgr9xHFCRGTmWISIqJ3bR3oBAPafK8O1ZrXMaYiIDIdFiIjaGenjBF8XO1xr1uDg+XK54xARGQyLEBG1I0kSbmu7eoyX0ROROWMRIqIOXT899nN2KWeZJiKzxSJERB2KGeKBftZKFFVf4yzTRGS2WISIqEN21kpMHM5ZponIvLEIEVGnJgcNAAAcza+UOQkRkWGwCBFRp0J8nAEAOcW1MichIjIMFiEi6lSwtxMAoLjmGirrm2ROQ0SkfyxCRNQpR1sr+Lv3AwBk86gQEZkhFiEi6tII7+unx3jlGBGZHxYhIurSiLbTYzwiRETmiEWIiLp0/YjQaRYhIjJDZl+EqqqqMH78eISFhWH06NFYt26d3JGITMoIn9YjQmeKa6HRcIZpIjIvVnIHMDQnJyfs3bsX9vb2qK+vx+jRo3HvvffCw8ND7mhEJiHQwwG2Vgo0NKuRX3EVgf0d5I5ERKQ3Zn9ESKlUwt7eHgDQ2NgIIQTvm0TUA0qFhCCv6+OEOGCaiMyL7EVo7969mDVrFnx9fSFJErZt29ZuHZVKhcDAQNjZ2SE6OhopKSk92kZVVRVCQ0Ph5+eH559/Hv3799dTeiLLwAHTRGSuZC9C9fX1CA0NhUql6vD1zZs3IyEhAatXr8bRo0cRGhqK6dOno7T0l3sfXR//89tHYWEhAMDV1RXHjx9Hbm4uPv/8c5SUlPTJ90ZkLq5PrJhdxCJEROZF9jFCM2bMwIwZMzp9fc2aNViyZAkWL14MAFi7di22b9+O9evXY+XKlQCAjIyMbm3Ly8sLoaGh2LdvH+6///4O12lsbERjY6P2eU0NTwUQjWy71QZPjRGRuZH9iFBXmpqakJ6ejri4OO0yhUKBuLg4HDp0qFvvUVJSgtra1r9iq6ursXfvXgQHB3e6/muvvQYXFxftw9/fv3ffBJEZuH5q7GLFVVxtapE5DRGR/hh1ESovL4darYaXl5fOci8vLxQXF3frPS5evIhJkyYhNDQUkyZNwpNPPokxY8Z0uv6qVatQXV2tfRQUFPTqeyAyBx6OtujvaAshgDMldXLHISLSG9lPjRlaVFRUt0+dAYCtrS1sbW0NF4jIRI30ccK+s43ILqpBmL+r3HGIiPTCqI8I9e/fH0qlst3g5pKSEnh7e8uUisgyXT89lnm5mlNQEJHZMOoiZGNjg4iICCQmJmqXaTQaJCYmIiYmxqDbVqlUCAkJQWRkpEG3Q2QqgttutfHZkXzc8loiln1+FP93KA+ni2o44zQRmSxJyPynXV1dHc6dOwcACA8Px5o1axAbGwt3d3cEBARg8+bNWLRoET766CNERUXh3XffxZdffons7Ox2Y4cMoaamBi4uLqiuroazs7PBt0dkrKquNmHZ58dwJPcKmtW6HxvOdlYYH+iOyEB3RA12w5iBrrCxMuq/s4jIzHX397fsRSg5ORmxsbHtli9atAgbN24EAHzwwQd48803UVxcjLCwMLz33nuIjo7uk3wsQkS6rjWrcSy/Cql5FUjNq8DRi5Wob1LrrGNrpUCYvyuiBrtjfKA7Iga5wdHW7IckEpERMZkiZOxYhIi61qLW4HRRLVLyKpCSewVpeZW4Ut+ks45CAkJ8nVuPGAW6I3KwO/o78qIEIjIcFiE9YREi6hkhBM6X1SMtrwIpbUeNCioa2q03ZIADIge1lqKoQHf4u/eDJEkyJCYic8Qi1EsqlQoqlQpqtRpnzpxhESLqhaLqBqTmVSI1t7UYdXTPMi9n27YxRq1jjYK9nKBQsBgR0c1hEdITHhEi0r+qq01Iy6tEattRo8xL1WjRcAA2EekPi5CesAgRGV5DkxrHCiq15Sj9YiWudjEAOzLQHeM4AJuIusAipCcsQkR9r0WtQVZRDVLaTqWl5lWi4jcDsJUKCSE+ztojRuMDOQCbiH7BIqQnLEJE8rs+ADs1rwKpua2n0y5VdjwAO0p7Os0dfm4cgE1kqViE9IRFiMg4FVU3/HLEKLcSOSXtB2B7O9u1XZXmhsjB7gjy5ABsIkvBItRLvGqMyLR0ZwC2Sz9rjB/UWooiA90xZqALB2ATmSkWIT3hESEi03R9AHZqbms5OprffgC2nXXbAOy2SR7HBbjBgQOwicwCi5CesAgRmYdmtQZZhTWtR4xyK5B2seMB2KPaZsBufbjBgwOwiUwSi5CesAgRmafWAdh1SGk7YpSSW4HLVe0HYA8d4KC9ZD8ykAOwiUwFi5CesAgRWY7CqgZtKUrNq8CZkrp26/i42LWWorZbgwz3dOQAbCIjxCKkJyxCRJarsr4JaRd/OWJ08nL7Adiu9m0DsNvK0WhfDsAmMgYsQnrCIkRE111takFGfpX2ZrJHL1ahobn9AOxwfzftEaPwAFcOwCaSAYtQL/HyeSK6kWa1BqcKa7STPKblVaDyarPOOkqFhNHXB2C3jTVyd7CRKTGR5WAR0hMeESKi7tJo2gZgt82AnZpX2eEA7GGejtpbg7QOwLaXIS2ReWMR0hMWISLqjctVDdojRqm5FThb2n4Atq+LnfZoUdRgdwwbwAHYRL3FIqQnLEJEpE8V9U1IaxtjlJJXiVOdDsD+5YjR6IEusFZyADZRT7AI6QmLEBEZ0tWmFhzLr9Jesn8sv/0A7H7WSoQHuGqPGIUHuMLehgOwibrCIqQnLEJE1Jea1RqcvFzddsl+JdIuVqDqNwOwrRQSRg10ab2ZbNtEj24cgE2kg0VIT1iEiEhOGo3AubI67RGj1NwKFFZfa7fecE9H7SX7kYPdMdC1nwxpiYwHi5CesAgRkbG5VHlVe8QoNa8C5zoYgD3QtR8iA3+Zz2iYpyNvDUIWhUWolziPEBGZior6Ju3RotS8CpwsrIH6NwOw3eytMT7wlyNGo3ydOQCbzBqLkJ7wiBARmZr6xrYB2G3l6FhBJa41a3TW6WetxLhBbQOwA90RHuCGfjZKmRIT6R+LkJ6wCBGRqWtq0eBkYbX2iFFqXiWqG9oPwB490AVRbfMZjR/kxgHYZNJYhPSERYiIzI1GI3C29NczYFegqIMB2EFejtpL9m8Z4gEvZzsZ0hLdHBYhPWERIiJzJ4TApcqGtqNFFUjJrcD5snqddawUEjY/EYOIQW4ypSTqme7+/uaMXEREFk6SJPi728Pf3R73jvMDAFypa0RqXutVaduOXcaV+iacLallESKzwyJERETteDja4s7R3rhztDcuXrmKn06XyB2JyCB47SQREXULx1GQOWIRIiIiIovFItQJlUqFkJAQREZGyh2FiEhW1yek5qU1ZI5YhDoRHx+PrKwspKamyh2FiIiIDIRFiIiIiCwWixAREXXp+q1aBYdLkxliESIiIiKLxSJERERd4mBpMmcsQkRERGSxWISIiIjIYrEIERFRl6S24dI8M0bmiEWIiIiILBaLEBERdQ9HS5MZYhEiIqIuXb9qjMgcWckdwNiJtr+AampqZE5CRCSPpoY6aBqv4mp9LT8LyWRc/1kVNziSKYkbrWHhLl26BH9/f7ljEBER0U0oKCiAn59fp6+zCN2ARqNBYWEhnJycIOnx+HBNTQ38/f1RUFAAZ2dnvb2vpeF+7D3uw97jPtQP7sfe4z78hRACtbW18PX1hULR+Uggnhq7AYVC0WWT7C1nZ2eL/2HVB+7H3uM+7D3uQ/3gfuw97sNWLi4uN1yHg6WJiIjIYrEIERERkcViEZKJra0tVq9eDVtbW7mjmDTux97jPuw97kP94H7sPe7DnuNgaSIiIrJYPCJEREREFotFiIiIiCwWixARERFZLBYhIiIislgsQgakUqkQGBgIOzs7REdHIyUlpcv1v/rqK4wYMQJ2dnYYM2YMfvjhhz5Katx6sh83btwISZJ0HnZ2dn2Y1vjs3bsXs2bNgq+vLyRJwrZt2274NcnJyRg3bhxsbW0xbNgwbNy40eA5jVlP92FycnK7n0NJklBcXNw3gY3Qa6+9hsjISDg5OcHT0xNz585FTk7ODb+On4u/uJl9yM/EG2MRMpDNmzcjISEBq1evxtGjRxEaGorp06ejtLS0w/UPHjyIhx56CL/73e9w7NgxzJ07F3PnzsXJkyf7OLlx6el+BFpnVC0qKtI+Ll682IeJjU99fT1CQ0OhUqm6tX5ubi5mzpyJ2NhYZGRkYPny5Xj88cexa9cuAyc1Xj3dh9fl5OTo/Cx6enoaKKHx27NnD+Lj43H48GHs3r0bzc3NuOOOO1BfX9/p1/BzUdfN7EOAn4k3JMggoqKiRHx8vPa5Wq0Wvr6+4rXXXutw/Xnz5omZM2fqLIuOjhZPPPGEQXMau57uxw0bNggXF5c+Smd6AIitW7d2uc6KFSvEqFGjdJbNnz9fTJ8+3YDJTEd39mFSUpIAICorK/skkykqLS0VAMSePXs6XYefi13rzj7kZ+KN8YiQATQ1NSE9PR1xcXHaZQqFAnFxcTh06FCHX3Po0CGd9QFg+vTpna5vCW5mPwJAXV0dBg0aBH9/f8yZMwenTp3qi7hmgz+L+hMWFgYfHx9MmzYNBw4ckDuOUamurgYAuLu7d7oOfxa71p19CPAz8UZYhAygvLwcarUaXl5eOsu9vLw6HSNQXFzco/Utwc3sx+DgYKxfvx7ffPMN/v3vf0Oj0eDWW2/FpUuX+iKyWejsZ7GmpgYNDQ0ypTItPj4+WLt2Lb7++mt8/fXX8Pf3x9SpU3H06FG5oxkFjUaD5cuXY8KECRg9enSn6/FzsXPd3Yf8TLwx3n2ezEpMTAxiYmK0z2+99VaMHDkSH330Ef7617/KmIwsSXBwMIKDg7XPb731Vpw/fx7vvPMOPv30UxmTGYf4+HicPHkS+/fvlzuKyeruPuRn4o3xiJAB9O/fH0qlEiUlJTrLS0pK4O3t3eHXeHt792h9S3Az+/G3rK2tER4ejnPnzhkiolnq7GfR2dkZ/fr1kymV6YuKiuLPIYBly5bh+++/R1JSEvz8/Lpcl5+LHevJPvwtfia2xyJkADY2NoiIiEBiYqJ2mUajQWJiok4z/7WYmBid9QFg9+7dna5vCW5mP/6WWq1GZmYmfHx8DBXT7PBn0TAyMjIs+udQCIFly5Zh69at+PnnnzF48OAbfg1/FnXdzD78LX4mdkDu0drm6osvvhC2trZi48aNIisrS/z+978Xrq6uori4WAghxMKFC8XKlSu16x84cEBYWVmJt956S5w+fVqsXr1aWFtbi8zMTLm+BaPQ0/34yiuviF27donz58+L9PR08eCDDwo7Oztx6tQpub4F2dXW1opjx46JY8eOCQBizZo14tixY+LixYtCCCFWrlwpFi5cqF3/woULwt7eXjz//PPi9OnTQqVSCaVSKXbu3CnXtyC7nu7Dd955R2zbtk2cPXtWZGZmiqefflooFArx008/yfUtyO4Pf/iDcHFxEcnJyaKoqEj7uHr1qnYdfi527Wb2IT8Tb4xFyIDef/99ERAQIGxsbERUVJQ4fPiw9rUpU6aIRYsW6az/5ZdfiqCgIGFjYyNGjRoltm/f3seJjVNP9uPy5cu163p5eYm77rpLHD16VIbUxuP6pdy/fVzfb4sWLRJTpkxp9zVhYWHCxsZGDBkyRGzYsKHPcxuTnu7DN954QwwdOlTY2dkJd3d3MXXqVPHzzz/LE95IdLT/AOj8bPFzsWs3sw/5mXhjkhBC9N3xJyIiIiLjwTFCREREZLFYhIiIiMhisQgRERGRxWIRIiIiIovFIkREREQWi0WIiIiILBaLEBEREVksFiEiIiLqc3v37sWsWbPg6+sLSZKwbdu2Hr/Hl19+ibCwMNjb22PQoEF48803e/weLEJEJKuXX34ZYWFhXa7z6KOPYu7cuXrb5o0+dPPy8iBJEjIyMvS2TSLSVV9fj9DQUKhUqpv6+h07duDhhx/G0qVLcfLkSfzzn//EO++8gw8++KBH78MiREQ61q5dCycnJ7S0tGiX1dXVwdraGlOnTtVZNzk5GZIk4fz5832csneKioowY8YMuWMQWbQZM2bgb3/7G+65554OX29sbMRzzz2HgQMHwsHBAdHR0UhOTta+/umnn2Lu3LlYunQphgwZgpkzZ2LVqlV444030JObZrAIEZGO2NhY1NXVIS0tTbts37598Pb2xpEjR3Dt2jXt8qSkJAQEBGDo0KE93o4QQqds9SVvb2/Y2trKsu2uNDU1yR2ByGgsW7YMhw4dwhdffIETJ07ggQcewJ133omzZ88CaC1KdnZ2Ol/Tr18/XLp0CRcvXuz2dliEiEhHcHAwfHx8dP7ySk5Oxpw5czB48GAcPnxYZ3lsbCyA1g+lp556Cp6enrCzs8PEiRORmpqqs64kSdixYwciIiJga2uL/fv3t9u+Wq1GQkICXF1d4eHhgRUrVnT5150QAgMGDMB///tf7bKwsDD4+Phon+/fvx+2tra4evUqgPanxlJSUhAeHg47OzuMHz8ex44da7edkydPYsaMGXB0dISXlxcWLlyI8vLyLvYksG7dOvj7+8Pe3h733HMP1qxZA1dXV+3r108Lfvzxxxg8eLD2Qz0/Px9z5syBo6MjnJ2dMW/ePJSUlGi/7vjx44iNjYWTkxOcnZ0RERGhLa4XL17ErFmz4ObmBgcHB4waNQo//PBDlzmJjE1+fj42bNiAr776CpMmTcLQoUPx3HPPYeLEidiwYQMAYPr06diyZQsSExOh0Whw5swZvP322wBaj/p2F4sQEbUTGxuLpKQk7fOkpCRMnToVU6ZM0S5vaGjAkSNHtEVoxYoV+Prrr7Fp0yYcPXoUw4YNw/Tp01FRUaHz3itXrsTrr7+O06dPY+zYse22/fbbb2Pjxo1Yv3499u/fj4qKCmzdurXTrJIkYfLkydriVllZidOnT6OhoQHZ2dkAgD179iAyMhL29vbtvr6urg533303QkJCkJ6ejpdffhnPPfeczjpVVVW47bbbEB4ejrS0NOzcuRMlJSWYN29ep7kOHDiApUuX4umnn0ZGRgamTZuGV199td16586dw9dff40tW7YgIyMDGo0Gc+bMQUVFBfbs2YPdu3fjwoULmD9/vvZrHn74Yfj5+SE1NRXp6elYuXIlrK2tAQDx8fFobGzE3r17kZmZiTfeeAOOjo6d5iQyRpmZmVCr1QgKCoKjo6P2sWfPHu2p+CVLlmDZsmW4++67YWNjg1tuuQUPPvggAECh6EG9ke/G90RkrNatWyccHBxEc3OzqKmpEVZWVqK0tFR8/vnnYvLkyUIIIRITEwUAcfHiRVFXVyesra3FZ599pn2PpqYm4evrK/7xj38IIYRISkoSAMS2bdt0trV69WoRGhqqfe7j46P9GiGEaG5uFn5+fmLOnDmd5n3vvffEqFGjhBBCbNu2TURHR4s5c+aIDz/8UAghRFxcnPjzn/+sXR+A2Lp1qxBCiI8++kh4eHiIhoYG7esffvihACCOHTsmhBDir3/9q7jjjjt0tllQUCAAiJycnA4zzZ8/X8ycOVNn2cMPPyxcXFx0vndra2tRWlqqXfbjjz8KpVIp8vPztctOnTolAIiUlBQhhBBOTk5i48aNHW53zJgx4uWXX+7wNSJj9et/k0II8cUXXwilUimys7PF2bNndR5FRUU6X9vS0iIuXbokGhsbxQ8//CAA6PybuhEeESKidqZOnYr6+nqkpqZi3759CAoKwoABAzBlyhTtOKHk5GQMGTIEAQEBOH/+PJqbmzFhwgTte1hbWyMqKgqnT5/Wee/x48d3ut3q6moUFRUhOjpau8zKyqrLrwGAKVOmICsrC2VlZdizZw+mTp2KqVOnIjk5Gc3NzTh48GC7gd7XXT8y9euxBjExMTrrHD9+HElJSTp/mY4YMQIAOh0onpOTg6ioKJ1lv30OAIMGDcKAAQN08vj7+8Pf31+7LCQkBK6urtp9mZCQgMcffxxxcXF4/fXXdTI89dRT+Nvf/oYJEyZg9erVOHHiRIf5iIxZeHg41Go1SktLMWzYMJ2Ht7e3zrpKpRIDBw6EjY0N/vOf/yAmJkbn39SNsAgRUTvDhg2Dn58fkpKSkJSUhClTpgAAfH194e/vj4MHDyIpKQm33XZbj9/bwcFB33ExZswYuLu7Y8+ePTpFaM+ePUhNTUVzczNuvfXWm37/uro6zJo1CxkZGTqPs2fPYvLkyb3KfjP74+WXX8apU6cwc+ZM/PzzzwgJCdGePnz88cdx4cIFLFy4EJmZmRg/fjzef//9XmUkMoS6ujrtvyUAyM3NRUZGBvLz8xEUFISHH34YjzzyCLZs2YLc3FykpKTgtddew/bt2wEA5eXlWLt2LbKzs5GRkYGnn34aX331Fd59990e5WARIqIOxcbGIjk5GcnJyTpHUyZPnowdO3YgJSVFOz5o6NChsLGxwYEDB7TrNTc3IzU1FSEhId3epouLC3x8fHDkyBHtspaWFqSnp3f5dZIkYdKkSfjmm29w6tQpTJw4EWPHjkVjYyM++ugjjB8/vtPCMXLkSJw4cULnarhfDwgHgHHjxuHUqVMIDAxs99dpZ+8bHBysM1gcQLvnneUpKChAQUGBdllWVhaqqqp09mVQUBCeeeYZ/Pjjj7j33nu1A0gBwN/fH0uXLsWWLVvw7LPPYt26dTfcLlFfS0tLQ3h4OMLDwwG0HukMDw/HSy+9BADYsGEDHnnkETz77LMIDg7G3LlzkZqaioCAAO17bNq0CePHj8eECRNw6tQpJCcnd3jktUv6Or9HROZl/fr1ol+/fsLKykoUFxdrl2/atEk4OTkJAKKwsFC7/Omnnxa+vr5ix44d4tSpU2LRokXCzc1NVFRUCCF+GSNUWVmps53fjhF6/fXXhbu7u9i6das4ffq0WLJkiXBycupyjJAQQrz77rtCqVSK6Oho7bI5c+YIpVIpVq5cqbMufjUeoba2VvTv318sWLBAnDp1Smzfvl0MGzZMZ4zQ5cuXxYABA8T9998vUlJSxLlz58TOnTvFo48+KlpaWjrMs3//fqFQKMTbb78tzpw5I9auXSs8PDyEq6trp9+7EEJoNBoRFhYmJk2aJNLT08WRI0dERESEmDJlihBCiKtXr4r4+HiRlJQk8vLyxP79+8XQoUPFihUrtP8fdu7cKS5cuCDS09NFdHS0mDdvXpf7jsiS8YgQEXUoNjYWDQ0NGDZsGLy8vLTLp0yZgtraWu1l9te9/vrruO+++7Bw4UKMGzcO586dw65du+Dm5taj7T777LNYuHAhFi1ahJiYGDg5OXU64dqvTZkyBWq1Wufo1dSpU9st+y1HR0d89913yMzMRHh4OF544QW88cYbOuv4+vriwIEDUKvVuOOOOzBmzBgsX74crq6unV6dMmHCBKxduxZr1qxBaGgodu7ciWeeeabdvCe/JUkSvvnmG7i5uWHy5MmIi4vDkCFDsHnzZgCt4yGuXLmCRx55BEFBQZg3bx5mzJiBV155BUDr9APx8fEYOXIk7rzzTgQFBeGf//znDfcfkaWShOjB9ItERHTTlixZguzsbOzbt0/uKETUxkruAERE5uqtt97CtGnT4ODggB07dmDTpk08OkNkZHhEiIjIQObNm4fk5GTU1tZiyJAhePLJJ7F06VK5YxHRr7AIERERkcXiYGkiIiKyWCxCREREZLFYhIiIiMhisQgRERGRxWIRIiIiIovFIkREREQWi0WIiIiILBaLEBEREVms/w+eg+cMc8FwSQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "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])" ] }, "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_21837/1767632406.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])" ] }, "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": [ "
" ] }, "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": "code", "execution_count": null, "metadata": { "id": "xQKrdPEMCpQc" }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "colab": { "provenance": [] }, "kernel_info": { "name": "python3" }, "kernelspec": { "display_name": "Python 3", "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" }, "nteract": { "version": "0.15.0" } }, "nbformat": 4, "nbformat_minor": 0 }