statistics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Describing a single set of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_friends = [100.0,49,41,40,25,21,21,19,19,18,18,16,15,15,15,15,14,14,13,13,13,13,12,12,11,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,8,8,8,8,8,8,8,8,8,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]\n",
    "\n",
    "friend_counts = Counter(num_friends)\n",
    "#print(friend_counts)\n",
    "\n",
    "xs = range(101)\n",
    "#print(xs)\n",
    "\n",
    "ys = [friend_counts[x] for x in xs]\n",
    "\n",
    "plt.bar(xs,ys)\n",
    "plt.axis([0,101,0,25])\n",
    "plt.title(\"Histogram of Friend Counts\")\n",
    "plt.xlabel(\"# of friends\")\n",
    "plt.ylabel(\"# of people\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = len(num_friends)\n",
    "assert num_points == 204"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0 1\n"
     ]
    }
   ],
   "source": [
    "largest_value = max(num_friends)\n",
    "smallest_value = min(num_friends)\n",
    "print(largest_value, smallest_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 8,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 9,\n",
       " 10,\n",
       " 10,\n",
       " 10,\n",
       " 10,\n",
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       " 10,\n",
       " 10,\n",
       " 10,\n",
       " 10,\n",
       " 10,\n",
       " 10,\n",
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       " 10,\n",
       " 10,\n",
       " 10,\n",
       " 11,\n",
       " 12,\n",
       " 12,\n",
       " 13,\n",
       " 13,\n",
       " 13,\n",
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       " 14,\n",
       " 14,\n",
       " 15,\n",
       " 15,\n",
       " 15,\n",
       " 15,\n",
       " 16,\n",
       " 18,\n",
       " 18,\n",
       " 19,\n",
       " 19,\n",
       " 21,\n",
       " 21,\n",
       " 25,\n",
       " 40,\n",
       " 41,\n",
       " 49,\n",
       " 100.0]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_values = sorted(num_friends)\n",
    "sorted_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smallest_value = sorted_values[0]\n",
    "smallest_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_smallest_value = sorted_values[1]\n",
    "second_smallest_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_largest_value = sorted_values[-2] \n",
    "second_largest_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Central Tendencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.333333333333333"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Mean\n",
    "def mean(x):\n",
    "    return sum(x)/len(x)\n",
    "\n",
    "mean(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Median\n",
    "def median(x):\n",
    "    n = len(x)\n",
    "    sorted_x = sorted(x)\n",
    "    midpoint = n//2\n",
    "    \n",
    "    if n%2 == 1:\n",
    "        return sorted_x[midpoint]\n",
    "    else:\n",
    "        lo=midpoint-1\n",
    "        hi=midpoint\n",
    "        \n",
    "        return (sorted_x[hi]+sorted_x[lo])/2\n",
    "    \n",
    "\n",
    "median(num_friends)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Quantile\n",
    "def quantile(x,p):\n",
    "    p_index = int(p*len(x))\n",
    "    return sorted(x)[p_index]\n",
    "\n",
    "quantile(num_friends, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 1]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#mode\n",
    "def mode(x):\n",
    "    counts = Counter(x)\n",
    "    max_count = max(counts.values())\n",
    "    \n",
    "    return [x_i for x_i,count in counts.items() if count==max_count]\n",
    "\n",
    "mode(num_friends) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dispersion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#range\n",
    "def data_range(x):\n",
    "    return max(x)-min(x)\n",
    "\n",
    "data_range(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "81.54351395730716"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def de_mean(x):\n",
    "    x_bar = mean(x)\n",
    "    return [x_i-x_bar for x_i in x]\n",
    "\n",
    "def variance(x):\n",
    "    n=len(x)\n",
    "    deviations = de_mean(x)\n",
    "    squared_deviations = [x_i*x_i for x_i in deviations]\n",
    "    return sum(squared_deviations)/(n-1)\n",
    "\n",
    "variance(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.03014473623248"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "def standard_deviation(x):\n",
    "    return math.sqrt(variance(x))\n",
    "\n",
    "standard_deviation(num_friends) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def interquartile_range(x):\n",
    "    return quantile(x,0.75)-quantile(x,0.25)\n",
    "\n",
    "interquartile_range(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.425435139573064"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "daily_minutes = [1,68.77,51.25,52.08,38.36,44.54,57.13,51.4,41.42,31.22,34.76,54.01,38.79,47.59,49.1,27.66,41.03,36.73,48.65,28.12,46.62,35.57,32.98,35,26.07,23.77,39.73,40.57,31.65,31.21,36.32,20.45,21.93,26.02,27.34,23.49,46.94,30.5,33.8,24.23,21.4,27.94,32.24,40.57,25.07,19.42,22.39,18.42,46.96,23.72,26.41,26.97,36.76,40.32,35.02,29.47,30.2,31,38.11,38.18,36.31,21.03,30.86,36.07,28.66,29.08,37.28,15.28,24.17,22.31,30.17,25.53,19.85,35.37,44.6,17.23,13.47,26.33,35.02,32.09,24.81,19.33,28.77,24.26,31.98,25.73,24.86,16.28,34.51,15.23,39.72,40.8,26.06,35.76,34.76,16.13,44.04,18.03,19.65,32.62,35.59,39.43,14.18,35.24,40.13,41.82,35.45,36.07,43.67,24.61,20.9,21.9,18.79,27.61,27.21,26.61,29.77,20.59,27.53,13.82,33.2,25,33.1,36.65,18.63,14.87,22.2,36.81,25.53,24.62,26.25,18.21,28.08,19.42,29.79,32.8,35.99,28.32,27.79,35.88,29.06,36.28,14.1,36.63,37.49,26.9,18.58,38.48,24.48,18.95,33.55,14.24,29.04,32.51,25.63,22.22,19,32.73,15.16,13.9,27.2,32.01,29.27,33,13.74,20.42,27.32,18.23,35.35,28.48,9.08,24.62,20.12,35.26,19.92,31.02,16.49,12.16,30.7,31.22,34.65,13.13,27.51,33.2,31.57,14.1,33.42,17.44,10.12,24.42,9.82,23.39,30.93,15.03,21.67,31.09,33.29,22.61,26.89,23.48,8.38,27.81,32.35,23.84]\n",
    "\n",
    "#covariance measures how two variables vary in tandem from their means\n",
    "def covariance(x,y):\n",
    "    n = len(x)\n",
    "    de_mean_x = de_mean(x)\n",
    "    de_mean_y = de_mean(y)\n",
    "    \n",
    "    dot_product = sum([x*y for x,y in zip(de_mean_x,de_mean_y)])\n",
    "    return dot_product/(n-1)\n",
    "\n",
    "covariance(num_friends,daily_minutes)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24736957366478218"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def correlation(x,y):\n",
    "    stdev_x = standard_deviation(x)\n",
    "    stdev_y = standard_deviation(y)\n",
    "    if stdev_x>0 and stdev_y>0:\n",
    "        return covariance(x,y)/stdev_x/stdev_y\n",
    "    else: \n",
    "        return 0\n",
    "    \n",
    "correlation(num_friends, daily_minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(num_friends,daily_minutes)\n",
    "plt.axis([0,110,0,100])\n",
    "plt.title(\"Correlation with outlier\")\n",
    "plt.xlabel(\"# of friends\")\n",
    "plt.ylabel(\"# of people\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "#remove outlier\n",
    "outlier = num_friends.index(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_friends_good = [x for i,x in enumerate(num_friends) if i!=outlier]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "daily_minutes_good = [x for i,x in enumerate(daily_minutes) if i!=outlier]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5736792115665573"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(num_friends_good, daily_minutes_good)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}