code/08.01-statistics_thinking.ipynb

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    "***\n",
    "***\n",
    "# Introduction to Statistical Thinking\n",
    "***\n",
    "***\n",
    "\n",
    "<img align=\"left\" style=\"padding-right:10px;\" width =\"200px\" src=\"./img/stats/preface2.png\">"
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    "#### Table of Contents\n",
    "\n",
    "1. [Introduction](./introduction.py)\n",
    "2. A Crash Course in Python\n",
    "3. [Visualizing Data](./visualizing_data.py)\n",
    "4. [Linear Algebra](./linear_algebra.py)\n",
    "5. [Statistics](./statistics.py)\n",
    "6. [Probability](./probability.py)\n",
    "7. [Hypothesis and Inference](./hypothesis_and_inference.py)\n",
    "8. [Gradient Descent](./gradient_descent.py)\n",
    "9. [Getting Data](./getting_data.py)\n",
    "10. [Working With Data](./working_with_data.py)\n",
    "11. [Machine Learning](./machine_learning.py)\n",
    "\n"
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    "\n",
    "12. [k-Nearest Neighbors](./nearest_neighbors.py)\n",
    "13. [Naive Bayes](./naive_bayes.py)\n",
    "14. [Simple Linear Regression](./simple_linear_regression.py)\n",
    "15. [Multiple Regression](./multiple_regression.py)\n",
    "16. [Logistic Regression](./logistic_regression.py)\n",
    "17. [Decision Trees](./decision_trees.py)\n",
    "18. [Neural Networks](./neural_networks.py)\n",
    "19. [Clustering](./clustering.py)\n",
    "20. [Natural Language Processing](./natural_language_processing.py)\n",
    "21. [Network Analysis](./network_analysis.py)\n",
    "22. [Recommender Systems](./recommender_systems.py)\n",
    "23. [Databases and SQL](./databases.py)\n",
    "24. [MapReduce](./mapreduce.py)\n",
    "25. Go Forth And Do Data Science"
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    "<img src = './img/stats/school.png' width = '800px' > \n",
    "\n",
    "**The School of Athens** by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City. https://en.wikipedia.org/wiki/Platonic_Academy"
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    "<img src = './img/stats/socrats2.png' width = '800px' > \n",
    "\n",
    "The School of Athens by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City. https://en.wikipedia.org/wiki/Platonic_Academy"
   ]
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    "<img src = './img/stats/plato.jpg' width = '150px' align = 'right'> \n",
    "\n",
    "# Plato & Typological Thinking\n",
    "\n",
    "- Pythagoras held that \n",
    "    - all things are number\n",
    "    - the cosmos comes from numerical principles. \n",
    "    \n",
    "`The theory of Forms` or `theory of Ideas` is a philosophical theory, concept, or world-view, attributed to Plato, that the `physical world` is not as real or true as timeless, absolute, unchangeable `ideas`."
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    "<img src = './img/stats/plato2.png' width = '150px' align = 'right'> \n",
    "\n",
    "- 真实的知识存在于普遍而永恒的法则之中。\n",
    "- The physical world of becoming is an imitation of the mathematical world of being.\n",
    "    - the realm of Being 本质世界(理念世界)\n",
    "        - perfect, eternal, and changeless forms, \n",
    "    - sensible world of becoming  现实世界\n",
    "        - imperfect\n"
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    "# Social Physics: Taking Physics as a Role Model\n",
    "- French social thinker **Henri de Saint-Simon** 1803 described the idea of describing society using laws similar to those of the physical and biological sciences.\n",
    "- His student and collaborator was **Auguste Comte**, a French philosopher, the founder of sociology, who first defined the term \n",
    "\n",
    "> Social physics is that science which occupies itself with social phenomena, considered in the same light as astronomical, physical, chemical, and physiological phenomena, that is to say as being subject to **natural and invariable laws**, the discovery of which is the special object of its researches.\n",
    "\n",
    "- Computational Social Science\n",
    "\n",
    "https://en.wikipedia.org/wiki/Social_physics"
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    "<img src = './img/stats/Adolphe_Quételet.jpg' width = '200px' align = 'right'> \n",
    "\n",
    "**Lambert Adolphe Jacques Quetelet** (1796-1874)\n",
    "- introducing statistical methods to the social sciences\n",
    "- in his book titled **Essays on Social Physics**, \n",
    "    - the concept of the \"average man\" \n",
    "    - characterized by the mean values \n",
    "    - follow a normal distribution. \n",
    "    - He collected data about many such variables.\n",
    "        - developed the body mass index scale\n",
    "        \n",
    "> “His goal was to understand the statistical laws underlying such phenomena as crime rates, marriage rates or suicide rates. He wanted to explain the values of these variables by other social factors”."
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    "\n",
    "<img src = './img/stats/darwin.jpg' width = '200px' align = 'right'> \n",
    "\n",
    "# **Population Thinking**\n",
    "\n",
    "\n",
    "**Charles Robert Darwin** (12 February 1809 – 19 April 1882)\n",
    "- the science of evolution.\n",
    "\n",
    "> favourable variations would make organisms better at surviving and passing the variations on to their offspring, while unfavourable variations would be lost.\n",
    "\n",
    "- Variation is the basis of natural seletion. \n",
    "\n",
    "> 在类型逻辑中平均数是主要的内容。在总体逻辑中重要的是差异，平均数只是总体的一个特征值，是探讨真实原因的手段，而不是原因本身。"
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   "source": [
    "# Statisticism  or Damn Lies\n",
    "\"统计至上主义\"天真地以为统计学是科学方法的完备基础。\n",
    "- 改进测量工具\n",
    "- 研究设计、概念化\n",
    "\n",
    "Duncan, O.D. 1984. Notes on Social Measurement, Historical and Critical. New York: Russell Sage Fundation, p.226."
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    "# The Paradigm of Demography\n",
    "\n",
    "\n",
    "Otis Dudley Duncan (1921-2004) 确立一种新的学术传统\n",
    "- 蔑视模仿自然科学试图寻找普遍规律的做法；\n",
    "- 记录和理解真实人口中的经验模式是第一要务；\n",
    "- 变异是人类社会的本质。\n",
    "    - 柏拉图：变异是对本质世界的拙劣复制。"
   ]
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    "<img src = './img/stats/aristotle2.png' width = '600px' > \n",
    "\n",
    "The School of Athens by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City. https://en.wikipedia.org/wiki/Platonic_Academy"
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   "source": [
    "## 本体论： 世界的本质\n",
    "<img src = './img/stats/galton.jpg' width = '200px' align = 'right'>\n",
    "> “我认为自然科学是以“挖掘”本质的世界中的真理为最终目的，这也是其精华所在。而社会科学是以“了解”形成的世界为最终目的。历史上很多人想在社会科学领域找到一种真理，能够适用于各个方面，并且做过许多这方面的尝试。我认为社会科学不应该是这样的。在社会科学中，我们的目的是要了解现实世界，而不是去挖掘永恒的真理。这可能和你们的想象不一样。......既然差异是世界的本质，那差异就应该是研究的对象。” --- 谢宇 \n",
    "\n",
    "- 高尔顿认为凯特莱的社会物理学用处不大，普通人不是万能的。\n",
    "    - 左手入冰，右手入火，平均温度？\n",
    "- 高尔顿说（社会）科学的探索必须关注变异和共变。\n",
    "    - variation & Co-variation\n"
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    "\n",
    "## 本体论： 世界的本质\n",
    "The measurements have both \n",
    "- a central tendency, or mean, and \n",
    "<img src = './img/stats/galton.jpg' width = '200px' align = 'right'>\n",
    "- a spread around this central value, or variance. \n",
    "    - In the late 1860s, Galton conceived of a measure to quantify normal variation: \n",
    "        - the **standard deviation**.\n",
    "- \"Regression to mediocrity\"\n"
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    "## 认识论： 人类知识的起源、本质、方法及局限\n",
    "\n",
    "谢宇：“你到底能知道什么，你怎样认识世界。\"\n",
    "- 自然科学追求永恒真理，关注典型现象；\n",
    "    - 典型现象 & 平均人\n",
    "- 社会科学关注所有个案组成的总体的状况。"
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   "source": [
    "## 方法论： 使用什么方法\n",
    "\n",
    "谢宇：“社会科学之所以复杂，是因为我们运用的数据是通过观察所得，而观察所得的数据必然受到外来因素的影响，这些外来因素都可能解释你的数据。“\n",
    "- 自然科学使用实验来隔离外来因素的影响；\n",
    "- “社会科学可以使用统计排除一些外来影响，但你不能排除所有的外来因素”。"
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    "## Three Basic Principles of Social Science Research\n",
    "\n",
    "- Variability Principle\n",
    "    - Social Grouping Principle\n",
    "        - Social Context Principle"
   ]
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   "source": [
    "------\n",
    "# Statistics for Describing Data\n",
    "------\n",
    "\n",
    "The mathematics and techniques with which we understand data."
   ]
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    "from collections import Counter\n",
    "#from linear_algebra import sum_of_squares, dot\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
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    "    def dot(v, w):\n",
    "        \"\"\"v_1 * w_1 + ... + v_n * w_n\"\"\"\n",
    "        return sum(v_i * w_i for v_i, w_i in zip(v, w))\n",
    "\n",
    "    def sum_of_squares(v):\n",
    "        \"\"\"v_1 * v_1 + ... + v_n * v_n\"\"\"\n",
    "        return dot(v, v)\n"
   ]
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    "daily_minutes = [1,68.77,51.25,52.08,38.36,44.54,57.13,\n",
    "                 51.4,41.42,31.22,34.76,54.01,38.79,\n",
    "                 47.59,49.1,27.66,41.03,36.73,48.65,28.12,\n",
    "                 46.62,35.57,32.98,35,26.07,23.77,39.73,\n",
    "                 40.57,31.65,31.21,36.32,20.45,21.93,26.02,\n",
    "                 27.34,23.49,46.94,30.5,33.8,24.23,21.4,27.94,\n",
    "                 32.24,40.57,25.07,19.42,22.39,18.42,46.96,23.72,\n",
    "                 26.41,26.97,36.76,40.32,35.02,29.47,30.2,31,\n",
    "                 38.11,38.18,36.31,21.03,30.86,36.07,28.66,\n",
    "                 29.08,37.28,15.28,24.17,22.31,30.17,25.53,\n",
    "                 19.85,35.37,44.6,17.23,13.47,26.33,35.02,\n",
    "                 32.09,24.81,19.33,28.77,24.26,31.98,25.73,\n",
    "                 24.86,16.28,34.51,15.23,39.72,40.8,26.06,\n",
    "                 35.76,34.76,16.13,44.04,18.03,19.65,32.62,\n",
    "                 35.59,39.43,14.18,35.24,40.13,41.82,35.45,\n",
    "                 36.07,43.67,24.61,20.9,21.9,18.79,27.61,27.21,\n",
    "                 26.61,29.77,20.59,27.53,13.82,33.2,25,33.1,36.65,\n",
    "                 18.63,14.87,22.2,36.81,25.53,24.62,26.25,18.21,\n",
    "                 28.08,19.42,29.79,32.8,35.99,28.32,27.79,35.88,29.06,\n",
    "                 36.28,14.1,36.63,37.49,26.9,18.58,38.48,24.48,\n",
    "                 18.95,33.55,14.24,29.04,32.51,25.63,22.22,19,\n",
    "                 32.73,15.16,13.9,27.2,32.01,29.27,33,13.74,20.42,\n",
    "                 27.32,18.23,35.35,28.48,9.08,24.62,20.12,35.26,\n",
    "                 19.92,31.02,16.49,12.16,30.7,31.22,34.65,13.13,\n",
    "                 27.51,33.2,31.57,14.1,33.42,17.44,10.12,24.42,\n",
    "                 9.82,23.39,30.93,15.03,21.67,31.09,33.29,22.61,\n",
    "                 26.89,23.48,8.38,27.81,32.35,23.84]\n"
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    "num_friends = [100,49,41,40,25,21,21,19,19,18,\n",
    "               18,16,15,15,15,15,14,14,13,13,\n",
    "               13,13,12,12,11,10,10,10,10,10,\n",
    "               10,10,10,10,10,10,10,10,10,10,\n",
    "               9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,\n",
    "               9,9,9,8,8,8,8,8,8,8,8,8,8,8,8,8\n",
    "               ,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,\n",
    "               6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,\n",
    "               6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,\n",
    "               5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,\n",
    "               4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,\n",
    "               3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,\n",
    "               2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,\n",
    "               1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,\n",
    "               1,1,1,1,1,1,1]"
   ]
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    "## Distribution and Histogram"
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    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_counts = Counter(map(int, daily_minutes))\n",
    "xs = range(69)\n",
    "ys = [time_counts[x] for x in xs]\n",
    "plt.bar(xs, ys)\n",
    "plt.axis([0,69,0,14])\n",
    "plt.title(\"Histogram of Time Counts\")\n",
    "plt.xlabel(\"# of Time\")\n",
    "plt.ylabel(\"# of people\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-09T01:06:51.611145Z",
     "start_time": "2019-06-09T01:06:51.240612Z"
    },
    "cell_style": "split",
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "friend_counts = Counter(num_friends)\n",
    "xs = range(101)\n",
    "ys = [friend_counts[x] for x in xs]\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",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can also draw them with ``plt.hist``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.169113Z",
     "start_time": "2019-04-14T06:42:26.971252Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(daily_minutes)\n",
    "plt.xlabel('Daily minutes')\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.414779Z",
     "start_time": "2019-04-14T06:42:27.171044Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(num_friends, bins= 30)\n",
    "plt.xlabel(\"# of friends\")\n",
    "plt.ylabel('Frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Unfortunately, this chart is still too difficult to interpret. \n",
    "- So you start generating some statistics. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-30T04:21:07.745547Z",
     "start_time": "2019-01-30T04:21:07.742911Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## From Max to Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.423459Z",
     "start_time": "2019-04-14T06:42:27.416704Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "204 100 1\n"
     ]
    }
   ],
   "source": [
    "num_points = len(num_friends)               # 204\n",
    "\n",
    "largest_value = max(num_friends)            # 100\n",
    "smallest_value = min(num_friends)           # 1\n",
    "\n",
    "print(num_points, largest_value, smallest_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.430493Z",
     "start_time": "2019-04-14T06:42:27.425689Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "sorted_values = sorted(num_friends)\n",
    "smallest_value = sorted_values[0]           # 1\n",
    "\n",
    "second_smallest_value = sorted_values[1]    # 1\n",
    "second_largest_value = sorted_values[-2]    # 49"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Mean, Median, Mode, and Quantile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.435402Z",
     "start_time": "2019-04-14T06:42:27.432205Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def mean(x):\n",
    "    return sum(x) / len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.440801Z",
     "start_time": "2019-04-14T06:42:27.437219Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean(num_friends) 7.333333333333333\n"
     ]
    }
   ],
   "source": [
    "print(\"mean(num_friends)\", mean(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.447458Z",
     "start_time": "2019-04-14T06:42:27.443094Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.333333333333333"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.461466Z",
     "start_time": "2019-04-14T06:42:27.449269Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def median(v):\n",
    "    \"\"\"finds the 'middle-most' value of v\"\"\"\n",
    "    n = len(v)\n",
    "    sorted_v = sorted(v)\n",
    "    midpoint = n // 2\n",
    "\n",
    "    if n % 2 == 1:\n",
    "        # if odd, return the middle value\n",
    "        return sorted_v[midpoint]\n",
    "    else:\n",
    "        # if even, return the average of the middle values\n",
    "        lo = midpoint - 1\n",
    "        hi = midpoint\n",
    "        return (sorted_v[lo] + sorted_v[hi]) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.467027Z",
     "start_time": "2019-04-14T06:42:27.463526Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median(num_friends) 6.0\n"
     ]
    }
   ],
   "source": [
    "print(\"median(num_friends)\", median(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.474744Z",
     "start_time": "2019-04-14T06:42:27.469684Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.481505Z",
     "start_time": "2019-04-14T06:42:27.477070Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def quantile(x, p):\n",
    "    \"\"\"returns the pth-percentile value in x\"\"\"\n",
    "    p_index = int(p * len(x))\n",
    "    return sorted(x)[p_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.490847Z",
     "start_time": "2019-04-14T06:42:27.483747Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quantile(num_friends, 0.10) 1\n",
      "quantile(num_friends, 0.25) 3\n",
      "quantile(num_friends, 0.75) 9\n",
      "quantile(num_friends, 0.90) 13\n"
     ]
    }
   ],
   "source": [
    "print(\"quantile(num_friends, 0.10)\", quantile(num_friends, 0.10))\n",
    "print(\"quantile(num_friends, 0.25)\", quantile(num_friends, 0.25))\n",
    "print(\"quantile(num_friends, 0.75)\", quantile(num_friends, 0.75))\n",
    "print(\"quantile(num_friends, 0.90)\", quantile(num_friends, 0.90))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.497871Z",
     "start_time": "2019-04-14T06:42:27.492951Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(num_friends, 75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.505162Z",
     "start_time": "2019-04-14T06:42:27.500135Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def mode(x):\n",
    "    \"\"\"returns a list, might be more than one mode\"\"\"\n",
    "    counts = Counter(x)\n",
    "    max_count = max(counts.values())\n",
    "    return [x_i for x_i, count in counts.items()\n",
    "            if count == max_count]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.511513Z",
     "start_time": "2019-04-14T06:42:27.507537Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mode(num_friends) [1, 6]\n"
     ]
    }
   ],
   "source": [
    "print(\"mode(num_friends)\", mode(num_friends))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.518299Z",
     "start_time": "2019-04-14T06:42:27.513508Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(np.bincount(num_friends))\n",
    "# Only the first occurrence is returned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:27.525117Z",
     "start_time": "2019-04-14T06:42:27.520336Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 22, 17, 20, 20, 17, 22, 15, 13, 18, 15,  1,  2,  4,  2,  4,  1,\n",
       "        0,  2,  2,  0,  2,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "        0,  0,  0,  0,  0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,\n",
       "        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.bincount(num_friends)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.069141Z",
     "start_time": "2019-04-14T06:42:27.527155Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ModeResult(mode=array([1]), count=array([22]))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "stats.mode(num_friends, axis=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.075349Z",
     "start_time": "2019-04-14T06:42:28.071972Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def data_range(x):\n",
    "    return max(x) - min(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.082122Z",
     "start_time": "2019-04-14T06:42:28.078026Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data_range(num_friends) 99\n"
     ]
    }
   ],
   "source": [
    "print(\"data_range(num_friends)\", data_range(num_friends))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T07:06:22.533491Z",
     "start_time": "2019-04-14T07:06:22.354263Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"ticks\", palette=\"pastel\")\n",
    "sns.boxplot(y = daily_minutes);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T07:06:25.246932Z",
     "start_time": "2019-04-14T07:06:25.070996Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"ticks\", palette=\"pastel\")\n",
    "sns.boxplot(y = num_friends);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Variance and Standard Deviation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$\\sigma = \\sqrt{\\frac{\\sum_{i=1}^N (x_i - \\overline{x})^2}{N-1} }$$\n",
    "\n",
    "$$\\sigma ^ 2 = \\frac{\\sum_{i=1}^N (x_i - \\overline{x})^2}{N-1} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.088746Z",
     "start_time": "2019-04-14T06:42:28.084295Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def de_mean(x):\n",
    "    \"\"\"translate x by subtracting its mean \n",
    "    so the result has mean 0\"\"\"\n",
    "    x_bar = mean(x)\n",
    "    return [x_i - x_bar for x_i in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.098460Z",
     "start_time": "2019-04-14T06:42:28.090915Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance(num_friends) 81.54351395730716\n"
     ]
    }
   ],
   "source": [
    "def variance(x):\n",
    "    \"\"\"assumes x has at least two elements\"\"\"\n",
    "    n = len(x)\n",
    "    deviations = de_mean(x)\n",
    "    return sum_of_squares(deviations) / (n - 1)\n",
    "\n",
    "print(\"variance(num_friends)\", variance(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.105298Z",
     "start_time": "2019-04-14T06:42:28.100576Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "81.14379084967321\n"
     ]
    }
   ],
   "source": [
    "print(np.var(num_friends))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.115622Z",
     "start_time": "2019-04-14T06:42:28.108322Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard_deviation(num_friends) 9.03014473623248\n"
     ]
    }
   ],
   "source": [
    "def standard_deviation(x):\n",
    "    return math.sqrt(variance(x))\n",
    "\n",
    "print(\"standard_deviation(num_friends)\", standard_deviation(num_friends))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.125171Z",
     "start_time": "2019-04-14T06:42:28.118612Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.007984838446012"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(num_friends)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Covariance, Correlation, and Scatter Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.132465Z",
     "start_time": "2019-04-14T06:42:28.128145Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "interquartile_range(num_friends) 6\n"
     ]
    }
   ],
   "source": [
    "def interquartile_range(x):\n",
    "    return quantile(x, 0.75) - quantile(x, 0.25)\n",
    "print(\"interquartile_range(num_friends)\", interquartile_range(num_friends))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.140684Z",
     "start_time": "2019-04-14T06:42:28.134285Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "covariance(num_friends, daily_minutes) 22.425435139573064\n"
     ]
    }
   ],
   "source": [
    "def covariance(x, y):\n",
    "    n = len(x)\n",
    "    return dot(de_mean(x), de_mean(y)) / (n - 1)\n",
    "\n",
    "print(\"covariance(num_friends, daily_minutes)\", covariance(num_friends, daily_minutes))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.153942Z",
     "start_time": "2019-04-14T06:42:28.143775Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 81.54351396,  22.42543514],\n",
       "       [ 22.42543514, 100.78589895]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(num_friends, daily_minutes) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:28.168433Z",
     "start_time": "2019-04-14T06:42:28.156807Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation(num_friends, daily_minutes) 0.24736957366478218\n"
     ]
    }
   ],
   "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 # if no variation, correlation is zero\n",
    "print(\"correlation(num_friends, daily_minutes)\", correlation(num_friends, daily_minutes))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:42:50.909207Z",
     "start_time": "2019-04-14T06:42:50.684823Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(num_friends, daily_minutes, \n",
    "            alpha = .1)\n",
    "plt.xlabel('number of friends')\n",
    "plt.ylabel('daily minutes')\n",
    "plt.title('outliers')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T06:58:37.422854Z",
     "start_time": "2019-04-14T06:58:35.643700Z"
    },
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"white\")\n",
    "g = sns.jointplot(num_friends, daily_minutes, \n",
    "                  kind=\"kde\", height=7, space=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-04-14T07:08:52.819938Z",
     "start_time": "2019-04-14T07:08:52.190012Z"
    },
    "cell_style": "center",
    "scrolled": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set(style=\"ticks\", palette=\"pastel\")\n",
    "sns.boxplot(x=num_friends, y=daily_minutes)\n",
    "sns.despine(offset=10, trim=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-12T04:35:33.605459Z",
     "start_time": "2018-09-12T04:35:33.598633Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.24736957],\n",
       "       [ 0.24736957,  1.        ]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(num_friends, daily_minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-12T04:36:06.053421Z",
     "start_time": "2018-09-12T04:36:06.047451Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.24736957366478224, 0.00036104739734502003)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats.stats import pearsonr   \n",
    "  \n",
    "pearsonr(num_friends, daily_minutes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-12T03:59:48.570216Z",
     "start_time": "2018-09-12T03:59:48.560977Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation(num_friends_good, daily_minutes_good) 0.5736792115665573\n"
     ]
    }
   ],
   "source": [
    "outlier = num_friends.index(100) # index of outlier\n",
    "\n",
    "num_friends_good = [x\n",
    "                    for i, x in enumerate(num_friends)\n",
    "                    if i != outlier]\n",
    "\n",
    "daily_minutes_good = [x\n",
    "                      for i, x in enumerate(daily_minutes)\n",
    "                      if i != outlier]\n",
    "\n",
    "\n",
    "print(\"correlation(num_friends_good, daily_minutes_good)\", \\\n",
    "      correlation(num_friends_good, daily_minutes_good))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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