10_descriptive_statistics.ipynb

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      "source": [
        "# Descriptive Statistics\n"
      ],
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      "source": [
        "Descriptive statistics are measures that summarize important features of data, often with a single number. Producing descriptive statistics is a common first step to take after cleaning and preparing a data set for analysis. We've already seen several examples of Descriptive statistics in earlier lessons, such as means and medians. In this lesson, we'll review some of these functions and explore several new ones."
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      "source": [
        "## Measures of Center"
      ],
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      "cell_type": "markdown",
      "source": [
        "Measures of center are statistics that give us a sense of the \"middle\" of a numeric variable. In other words, centrality measures give you a sense of a typical value you'd expect to see. Common measures of center include the mean, median and mode.\n",
        "\n",
        "The mean is simply an average: the sum of the values divided by the total number of records. As we've seen in previous lessons we can use df.mean() to get the mean of each column in a DataFrame:"
      ],
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      "cell_type": "code",
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
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      "source": [
        "mtcars = pd.read_csv(\"../input/mtcars/mtcars.csv\")\n",
        "mtcars =  mtcars.rename(columns={'Unnamed: 0': 'model'})\n",
        "mtcars.index = mtcars.model\n",
        "del mtcars[\"model\"]\n",
        "\n",
        "mtcars.head()"
      ],
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        {
          "execution_count": 26,
          "output_type": "execute_result",
          "data": {
            "text/plain": "                    mpg  cyl   disp   hp  drat     wt   qsec  vs  am  gear  \\\nmodel                                                                        \nMazda RX4          21.0    6  160.0  110  3.90  2.620  16.46   0   1     4   \nMazda RX4 Wag      21.0    6  160.0  110  3.90  2.875  17.02   0   1     4   \nDatsun 710         22.8    4  108.0   93  3.85  2.320  18.61   1   1     4   \nHornet 4 Drive     21.4    6  258.0  110  3.08  3.215  19.44   1   0     3   \nHornet Sportabout  18.7    8  360.0  175  3.15  3.440  17.02   0   0     3   \n\n                   carb  \nmodel                    \nMazda RX4             4  \nMazda RX4 Wag         4  \nDatsun 710            1  \nHornet 4 Drive        1  \nHornet Sportabout     2  ",
            "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>mpg</th>\n      <th>cyl</th>\n      <th>disp</th>\n      <th>hp</th>\n      <th>drat</th>\n      <th>wt</th>\n      <th>qsec</th>\n      <th>vs</th>\n      <th>am</th>\n      <th>gear</th>\n      <th>carb</th>\n    </tr>\n    <tr>\n      <th>model</th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n      <th></th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <td>Mazda RX4</td>\n      <td>21.0</td>\n      <td>6</td>\n      <td>160.0</td>\n      <td>110</td>\n      <td>3.90</td>\n      <td>2.620</td>\n      <td>16.46</td>\n      <td>0</td>\n      <td>1</td>\n      <td>4</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <td>Mazda RX4 Wag</td>\n      <td>21.0</td>\n      <td>6</td>\n      <td>160.0</td>\n      <td>110</td>\n      <td>3.90</td>\n      <td>2.875</td>\n      <td>17.02</td>\n      <td>0</td>\n      <td>1</td>\n      <td>4</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <td>Datsun 710</td>\n      <td>22.8</td>\n      <td>4</td>\n      <td>108.0</td>\n      <td>93</td>\n      <td>3.85</td>\n      <td>2.320</td>\n      <td>18.61</td>\n      <td>1</td>\n      <td>1</td>\n      <td>4</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <td>Hornet 4 Drive</td>\n      <td>21.4</td>\n      <td>6</td>\n      <td>258.0</td>\n      <td>110</td>\n      <td>3.08</td>\n      <td>3.215</td>\n      <td>19.44</td>\n      <td>1</td>\n      <td>0</td>\n      <td>3</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <td>Hornet Sportabout</td>\n      <td>18.7</td>\n      <td>8</td>\n      <td>360.0</td>\n      <td>175</td>\n      <td>3.15</td>\n      <td>3.440</td>\n      <td>17.02</td>\n      <td>0</td>\n      <td>0</td>\n      <td>3</td>\n      <td>2</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
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      "source": [
        "mtcars.mean()                 # Get the mean of each column"
      ],
      "metadata": {
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      "execution_count": null,
      "outputs": [
        {
          "execution_count": 30,
          "output_type": "execute_result",
          "data": {
            "text/plain": "mpg      20.090625\ncyl       6.187500\ndisp    230.721875\nhp      146.687500\ndrat      3.596563\nwt        3.217250\nqsec     17.848750\nvs        0.437500\nam        0.406250\ngear      3.687500\ncarb      2.812500\ndtype: float64"
          },
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    },
    {
      "cell_type": "markdown",
      "source": [
        "We can also get the means of each row by supplying an axis argument:"
      ],
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    },
    {
      "cell_type": "code",
      "source": [
        "mtcars.mean(axis=1)           # Get the mean of each row"
      ],
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      "execution_count": null,
      "outputs": [
        {
          "execution_count": 28,
          "output_type": "execute_result",
          "data": {
            "text/plain": "model\nMazda RX4              29.907273\nMazda RX4 Wag          29.981364\nDatsun 710             23.598182\nHornet 4 Drive         38.739545\nHornet Sportabout      53.664545\nValiant                35.049091\nDuster 360             59.720000\nMerc 240D              24.634545\nMerc 230               27.233636\nMerc 280               31.860000\nMerc 280C              31.787273\nMerc 450SE             46.430909\nMerc 450SL             46.500000\nMerc 450SLC            46.350000\nCadillac Fleetwood     66.232727\nLincoln Continental    66.058545\nChrysler Imperial      65.972273\nFiat 128               19.440909\nHonda Civic            17.742273\nToyota Corolla         18.814091\nToyota Corona          24.888636\nDodge Challenger       47.240909\nAMC Javelin            46.007727\nCamaro Z28             58.752727\nPontiac Firebird       57.379545\nFiat X1-9              18.928636\nPorsche 914-2          24.779091\nLotus Europa           24.880273\nFord Pantera L         60.971818\nFerrari Dino           34.508182\nMaserati Bora          63.155455\nVolvo 142E             26.262727\ndtype: float64"
          },
          "metadata": {}
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    },
    {
      "cell_type": "markdown",
      "source": [
        "The median of a distribution is the value where 50% of the data lies below it and 50% lies above it. In essence, the median splits the data in half. The median is also known as the 50% percentile since 50% of the observations are found below it. As we've seen previously, you can get the median using the df.median() function:"
      ],
      "metadata": {
        "id": "kmvutr243nZH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars.median()                 # Get the median of each column"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:25.085003Z",
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      "execution_count": null,
      "outputs": [
        {
          "execution_count": 5,
          "output_type": "execute_result",
          "data": {
            "text/plain": "mpg      19.200\ncyl       6.000\ndisp    196.300\nhp      123.000\ndrat      3.695\nwt        3.325\nqsec     17.710\nvs        0.000\nam        0.000\ngear      4.000\ncarb      2.000\ndtype: float64"
          },
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      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Again, we could get the row medians across each row by supplying the argument axis=1.\n",
        "\n",
        "Although the mean and median both give us some sense of the center of a distribution, they aren't always the same. The median always gives us a value that splits the data into two halves while the mean is a numeric average so extreme values can have a significant impact on the mean. In a symmetric distribution, the mean and median will be the same. Let's investigate with a density plot:"
      ],
      "metadata": {
        "id": "HQK18Zg83nZH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "norm_data = pd.DataFrame(np.random.normal(size=100000))\n",
        "\n",
        "norm_data.plot(kind=\"density\",\n",
        "              figsize=(10,10));\n",
        "\n",
        "\n",
        "plt.vlines(norm_data.mean(),     # Plot green line at mean\n",
        "           ymin=0,\n",
        "           ymax=0.4,\n",
        "           linewidth=5.0,\n",
        "          color=\"green\");\n",
        "\n",
        "plt.vlines(norm_data.median(),   # Plot red line at median\n",
        "           ymin=0,\n",
        "           ymax=0.4,\n",
        "           linewidth=2.0,\n",
        "           color=\"red\");"
      ],
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        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 720x720 with 1 Axes>",
            "image/png": 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NQOQMFBf19we9Zq04ssa6NQBbQVgDEDmDk4Vw1L8z2GnQzqakKiuMHaEAtoSwBiByBqbmVWFST0uwYS1RYepuSWqAkTUAW0BYAxA5A5Pz6m6uVVUi+K+4nuZajcwQ1gBsXvDfZABQYgNTC4GdXLBad3NSZ2bSQZcBIMQIawAiZ2Ay+B5rnq7mWo2m0srnXdClAAgpwhqASEkv5TQ2uxj4TlBPV1ONlnJOk/OZoEsBEFKENQCR4rXJCHonqKeruVDHCFOhADaJsAYgUrwea7vKZBq0uzkpSaxbA7BphDUAkTI4WWyIW2ZhjR2hADaLsAYgUgamFlRdWaH2hpqgS5EktTbUKFFhGkkxsgZgcwhrACJlYHJefTtqVVFhQZciqdAYt7OxhmlQAJtGWAMQKYNTC2WzE9TT1ZxkgwGATSOsAYiUoekF9ZZJQ1xPd3Mt06AANo2wBiAyFjI5Tc5l1BvwmaCrdTYVRtacozEugI0jrAGIjDPFHZfeDsxy0d2c1Hwmp1Q6G3QpAEKIsAYgMoanC1ONPWU2sta13L6DqVAAG0dYAxAZw8WRtZ7m8gpry73WWLcGYBMIawAiY3h6QWZSZ3N59FjzdDbRGBfA5hHWAETGmem02hpqVFOZCLqUV/DCGr3WAGwGYQ1AZAzPLJTdejVJqq6sUFtDjUaZBgWwCYQ1AJExPL2gnjLbCerpaq5Z3gABABtBWAMQCc45nZlJl+XImiR1NSUZWQOwKYQ1AJEws7Ck+Uyu7HqseTqbkhqbXQy6DAAhRFgDEAneFGO5nV7g6WxKanIuo8VsLuhSAIQMYQ1AJAxPF08vKNOw1lXcETqWYnQNwMYQ1gBEgnfUVE9LeU6DdjQVer+xbg3ARhHWAETC0HRaVQlTW315NcT1eEdOjTKyBmCDCGsAIuHMzIK6m2tVUWFBl7KmzkaOnAKwOYQ1AJEwPL1QtjtBJamlrkrVlRUaI6wB2CDCGoBIGJ4u3x5rkmRm6myqYWQNwIYR1gCEnnNOY7Pp5TM4yxWNcQFsBmENQOhNzS9pKefU2VSemws8HU1JNhgA2DDCGoDQG5stjFaFZWTNORd0KQBChLAGIPS80apyH1nrbKrRfCan2cVs0KUACBHCGoDQ89aBdTSW98ha5/IpBqxbA7B+hDUAoeeFn/bGch9ZK/Zam2HdGoD1I6wBCL3R1KJa6qqUrEoEXcpFeWGNHaEANoKwBiD0xmbTyycElDNvTR291gBsBGENQOiNphaXD0ovZ3XVlWpMVrJmDcCGENYAhN5YKl32mws8XU1JRtYAbAhhDUCo5fNOY7OLZd+2w9NJY1wAG0RYAxBqU/MZZfOu7Bviejo5cgrABhHWAISaN0rVUeZtOzydTTUam11UPs8pBgDWh7AGINRGi0dNdYRkZK2rOalc3unsHFOhANaHsAYg1LydlWFZs+ZthBhj3RqAdfI1rJnZbWZ21MyOm9lH13j9Q2b2rJk9ZWbfMbMDK1771eJ9R83sVj/rBBBeXugp99MLPF3NNMYFsDG+hTUzS0i6V9I7JB2Q9L6VYazos8651zrnrpf0KUm/X7z3gKQ7JV0t6TZJf1x8PwB4hdHZtHbUVammMhxfETTGBbBRfo6s3STpuHPuhHMuI+kBSXesvMA5l1rxsF6St+L2DkkPOOcWnXMnJR0vvh8AvMJoajE0O0Elqb2hRmaifQeAdav08b17JQ2seDwo6ebVF5nZhyV9RFK1pH+z4t5HVt3bu8a9d0m6S5J27dpVkqIBhMtYKh2azQWSVJmoUFtDjUZnGFkDsD5+jqzZGs+9aq+6c+5e59zlkn5F0q9v8N77nHMHnXMH29vbt1QsgHAaTS2qMyTr1TxdTcnlXawAcCl+hrVBSf0rHvdJGr7I9Q9Ievcm7wUQQ/m80/i5cJwLulJnU41GGFkDsE5+hrXHJe0zsz1mVq3ChoEHV15gZvtWPHyXpBeLPz8o6U4zqzGzPZL2SXrMx1oBhNDEXEa5EJ1e4OlsSmpsljVrANbHtzVrzrmsmd0t6WFJCUn3O+cOm9k9kg455x6UdLeZvVXSkqQpSR8s3nvYzL4g6YikrKQPO+dyftUKIJy89hdhOcTd09mU1ORcRovZXGh2sQIIjp8bDOSce0jSQ6ue+9iKn3/xIvf+tqTf9q86AGE3NhuuhrierqbzjXH7d9YFXA2AcscJBgBCy2uIG6bdoJKW19jRGBfAehDWAISW16usvSFcI2veGjt6rQFYD8IagNAanU2rtb5a1ZXh+irzpkE5xQDAeoTrGw4AVghbQ1xPS12Vqisrlg+hB4CLIawBCK2x2UV1hKwhriSZWaHXGmENwDoQ1gCE1mgqHbqdoJ7OxiQbDACsC2ENQCjl8k7js+E6xH2lzuYkGwwArAthDUAoTZxbVN6Fr22HxxtZc+5Vxx4DwCsQ1gCEkjcqFcY1a5LU1Vyj+UxOs4vZoEsBUOYIawBC6fzpBSEdWVs+xYB1awAujrAGIJTCPrLmhbWRGdatAbg4whqAUBpNpWUmtYc8rLEjFMClENYAhNJoKq3W+hpVJcL5Nea1HKHXGoBLCee3HIDYC3OPNUmqq65UY7KSNWsALomwBiCURlOLy2dshlVXU5KRNQCXRFgDEEpjs+E8F3SlziYa4wK4NMIagNDJZPM6ey4T6mlQqRDWmAYFcCmENQChM36uMBoV9mnQzqYajc0uKp/nFAMAF0ZYAxA6XruLsDbE9XQ1J5XNO03MZYIuBUAZI6wBCJ3RmUJY6wj5NGhHI73WAFwaYQ1A6HjhJuzToF3NhDUAl0ZYAxA6o7OLqkqYdtRVB13KltAYF8B6ENYAhM5oKq2OxqQqKizoUrakvaFGZqJ9B4CLIqwBCJ3RVDr069UkqTJRobaGmuU1eACwFsIagNCJwukFns6mGo3OEtYAXBhhDUDoFM4FjUZY62pKaoSRNQAXQVgDECrzmaxm09lITINKUk9LrYamF4IuA0AZI6wBCBVvMX5UpkF7W2o1m84qlV4KuhQAZYqwBiBUonJ6gad3R60kaWiK0TUAayOsAQiV82EtGtOgvS2ENQAXR1gDECqRHVlj3RqACyCsAQiV0dSi6qoTaqipDLqUkmirr1F1ZQVhDcAFEdYAhIrXtsMs3KcXeCoqTL0ttUyDArggwhqAUCkcNRWN9Wqe3pZaDTKyBuACCGsAQmU0taiu5misV/MwsgbgYghrAELDORep0ws8vTtqdfbcotJLuaBLAVCGCGsAQmNmYUmL2Xwkp0ElaZipUABrIKwBCI3l0wuiNg1K+w4AF0FYAxAaUeux5qExLoCLIawBCI3lsNYYrbDW1ZxUhTGyBmBthDUAoeGFtY6IHDXlqUpUqKspycgagDUR1gCExmhqUS11VUpWJYIupeR6d9BrDcDaCGsAQmMklY7cFKiHXmsALoSwBiA0RlNpdUZsJ6ind0etRlJpZXP5oEsBUGYIawBCYzSVVmfEeqx5elvqlMs7jc4uBl0KgDJDWAMQCtlcXuOz0TtqyrPca42pUACrENYAhMLEXEZ5F70ea57lXmvT8wFXAqDcENYAhMLITDQb4nrOHzmVDrgSAOWGsAYgFLwea10RDWu11QntrK+mMS6AVyGsAQiF80dNRXODgST1tCQ5zB3AqxDWAITCaGpRiQpTa0OEw1pzLWENwKsQ1gCEwkgqrfaGGiUqLOhSfNNTbIzrnAu6FABlhLAGIBSi3BDX09tSq7lMTql0NuhSAJQRX8Oamd1mZkfN7LiZfXSN1z9iZkfM7Bkz+7qZXbbitZyZPVX886CfdQIof1FuiOvxeq0xFQpgJd/CmpklJN0r6R2SDkh6n5kdWHXZk5IOOueulfQ3kj614rUF59z1xT+3+1UngHAYmUlHtiGup6eFxrgAXs3PkbWbJB13zp1wzmUkPSDpjpUXOOe+6ZzzOkA+IqnPx3oAhNRCcWowqj3WPD0thX+/4RnCGoDz/AxrvZIGVjweLD53IT8r6csrHifN7JCZPWJm717rBjO7q3jNofHx8a1XDKAsnW/bEe2w1lZfo+pEBb3WALxCpY/vvdaWrTW3OJnZ+yUdlPTmFU/vcs4Nm9leSd8ws2edcy+94s2cu0/SfZJ08OBBtk8BERX1hrieigpTd0uSUwwAvIKfI2uDkvpXPO6TNLz6IjN7q6Rfk3S7c27Re945N1z85wlJ35J0g4+1AihjIzFoiOuh1xqA1fwMa49L2mdme8ysWtKdkl6xq9PMbpD0aRWC2tiK53eYWU3x5zZJb5R0xMdaAZSxsVTh97iot+6QCjtC2WAAYCXfpkGdc1kzu1vSw5ISku53zh02s3skHXLOPSjp9yQ1SPprM5Ok08Wdn6+R9Gkzy6sQKD/pnCOsATE1kkqrtiqhxho/V26Uh56WWo3OprWUy6sqQStMAP6uWZNz7iFJD6167mMrfn7rBe77rqTX+lkbgPAYTRXadhR/qYu03paknCu0KunfWRd0OQDKAL+2ASh7o6m0OiLeENfj9Vpj3RoAD2ENQNkbSUW/Ia5nuTEuYQ1AEWENQFlzzmk0tRj5Hmue7mIo9XbAAgBhDUBZm55fUiabj01Yq6uuVGOycnkHLAAQ1gCUtdHZeDTEXamzKamRGUbWABQQ1gCUNS+0xKEhrqezqWY5pAIAYQ1AWVtuiBuzkTWmQQF4CGsAypq30L4jViNrSY2m0srnOfIYAGENQJkbTaW1s75aNZWJoEvZNl1NSWXzTpPzmaBLAVAGCGsAylqcGuJ6vPV5bDIAIBHWAJS50dRibBrierz1eWNsMgAgwhqAMjeSSquzMZ5hbWSGTQYACGsAythSLq+z5xbVGbORtfbGGpkVpoABgLAGoGydPbco5+LVY02SqhIVaq2vYRoUgCTCGoAy5i2wj9PpBZ7Opho2GACQRFgDUMZGY9gQ19PVlFz+9wcQb4Q1AGXLW7MVx7DWUWyMCwCENQBlazSVVmWFqbW+OuhStl1nU40m5jLKZPNBlwIgYIQ1AGVrpNgQt6LCgi5l23nr9MbPMRUKxB1hDUDZGkvFr22H53yvNaZCgbgjrAEoW3FsiOtZPsWAdWtA7BHWAJSt0Zl07I6a8iyfD0pYA2KPsAagLM0tZjW7mFVHzBrienbUVauywjQ2y5o1IO4IawDKkte2Io4NcSWposLU3lijMXqtAbFHWANQlryGsHENa5LU0ciRUwAIawDKlDey1hHjsNbemNQ406BA7BHWAJSl5WnQmG4wkKSOphrWrAEgrAEoTyOptOqrE2qoqQy6lMB0NNZoklMMgNgjrAEoS3FuiOvpKPaYO8spBkCsEdYAlKU4N8T1dDQW2pYwFQrEG2ENQFkaTcW3Ia7H6zHHKQZAvBHWAJQd55zGUouxbYjr8aZBGVkD4o2wBqDsTM5llMnlY91jTZLaGqplRlgD4o6wBqDseA1xO2Me1ioTFWqtr9Y4jXGBWCOsASg7Xo+1uIc1qdAYlyOngHgjrAEoOzTEPa+TxrhA7BHWAJSdkWJYa2+I9wYDifNBARDWAJSh0dSi2hqqVV3JV1RHY1Jnz2WUy7ugSwEQEL4JAZSd0VR6uW1F3HU01SiXd5qcywRdCoCAENYAlB0a4p53/hQDpkKBuFpXWDOzL5rZu8yMcAfAd6OptDpj3hDX005jXCD21hu+/kTSf5D0opl90syu8rEmADGWyeZ19lyGth1F3sjaOO07gNhaV1hzzn3NOfeTkl4n6ZSkr5rZd83sp82sys8CAcTL+Dka4q7UzjQoEHvrntY0s1ZJPyXp5yQ9KekPVAhvX/WlMgCxNDJT7LFGWJMkJasSaq6tWj7VAUD8VK7nIjP7W0lXSfoLST/qnDtTfOnzZnbIr+IAxM9Yscda3A9xX4lea0C8rSusSfrfzrmHVj5hZjXOuUXn3EEf6gIQU15DXEbWzuvgFAMg1tY7Dfpbazz3vVIWAgBSoSFuVcK0s7466FLKRgfngwKxdtGRNTPrktQrqdbMbpBkxZeaJNX5XBuAGPIa4prZpS+OiY7GGo3PLso5x98LEEOXmga9VYVNBX2Sfn/F87OS/ptPNQGIMRrivlp7Y40yubxmFpbUUseIIxA3Fw1rzrnPSPqMmf0759wXt6mjAcK1AAAgAElEQVQmADE2kkrrqq7GoMsoKx1N5xvjEtaA+LnUNOj7nXN/KWm3mX1k9evOud9f4zYA2LSx1KLefGV70GWUleUjp1KLurKTIAvEzaWmQeuL/2zwuxAAOLeY1bnFLA1xV+F8UCDeLjUN+uniP39jM29uZrep0Dw3oUL7j0+uev0jKjTZzUoal/QzzrmXi699UNKvFy/9reKULIAIoyHu2lZOgwKIn/Ue5P4pM2sysyoz+7qZnTWz91/inoSkeyW9Q9IBSe8zswOrLntS0kHn3LWS/kbSp4r37pT0cUk3S7pJ0sfNbMdG/sUAhA8NcdfWUFOpuuoE7TuAmFpvn7W3O+dSkv6tpEFJV0r65Uvcc5Ok4865E865jKQHJN2x8gLn3Dedc/PFh4+osOtUKuxC/apzbtI5N6XCkVa3rbNWACFFQ9wL4xQDIL7WG9a8w9rfKelzzrnJddzTK2lgxePB4nMX8rOSvrzJewFEgHf+JWvWXq2jMck0KBBT6w1rXzKzFyQdlPR1M2uXdKlf8dbq3OjWvLAwpXpQ0u9t5F4zu8vMDpnZofHx8UuUA6DcjabSaqypVH3Nek/Ci4/2pkJjXADxs66w5pz7qKQ3qLC+bEnSnFZNaa5hUFL/isd9koZXX2Rmb5X0a5Jud84tbuRe59x9zrmDzrmD7e1s9QfCbjSVVicNcdfU0VizvKYPQLxs5NfX16jQb23lPX9+kesfl7TPzPZIGpJ0p6T/sPKC4hFWn5Z0m3NubMVLD0v6nRWbCt4u6Vc3UCuAEBpJpdXJ5oI1dTQmNZfJaW4xy8gjEDPr+i/ezP5C0uWSnpKUKz7tdJGw5pzLmtndKgSvhKT7nXOHzeweSYeccw+qMO3ZIOmvi+fdnXbO3e6cmzSz31Qh8EnSPetcJwcgxMZSi7p5786gyyhL53utLWoPYQ2IlfX+F39Q0gHn3Jprzi7EOfeQpIdWPfexFT+/9SL33i/p/o18HoDwyuddYRqUzQVr8tqZjKXS2tNWf4mrAUTJejcYPCepy89CAMTbxFxG2byjbccFdDTSGBeIq/WOrLVJOmJmj0la/qZwzt3uS1UAYme0uHieNWtrWzkNCiBe1hvWPuFnEQBwPqwxsraWlroqVScqaIwLxNC6wppz7ttmdpmkfc65r5lZnQqbBgCgJGiIe3FmpvbGGo1z5BQQO+s9G/TnVTi789PFp3ol/b1fRQGIn5FUWmZSeyPToBfS3ljDNCgQQ+vdYPBhSW+UlJIk59yLkjr8KgpA/Iyl0mprqFFVYr1fS/HD+aBAPK33W3GxeBi7JKnYGHdDbTwA4GJoiHtpHU2MrAFxtN6w9m0z+2+Sas3sbZL+WtKX/CsLQNyMphZp23EJnY1JTc8vaTGbu/TFACJjvWHto5LGJT0r6RdUaHT7634VBSB+RlNpdRDWLsprjMuB7kC8rHc3aN7M/l7S3zvnxn2uCUDMLGZzmpzLMLJ2CSsb4/btqAu4GgDb5aIja1bwCTM7K+kFSUfNbNzMPnax+wBgI8aW23awZu1ivJ2yY7TvAGLlUtOg/0WFXaA3OudanXM7Jd0s6Y1m9v/4Xh2AWKAh7vqcnwZlRygQJ5cKax+Q9D7n3EnvCefcCUnvL74GAFtGQ9z1aa2vUYWd//sCEA+XCmtVzrmzq58srlur8qckAHEzUhxZY83axSUqTG0N9FoD4uZSYS2zydcAYN3GUmlVV1aopY7fAS+FXmtA/FxqN+h1ZpZa43mTxK/AAErCa4hrZkGXUvY6GpMamWFkDYiTi4Y15xyHtQPw3ZmZtLqbaoMuIxQ6Gmv0zOBM0GUA2EYcwgcgcCMzaXU1M1i/Hh2NNZqYW1Q2lw+6FADbhLAGIFDOOY2k0uomrK1Le1NSzkkTcywbBuKCsAYgUFPzS8pk84ysrVMHjXGB2CGsAQjUmZkFSWJkbZ2WwxrtO4DYIKwBCJS3s7GrmQ0G6+Eddk/7DiA+CGsAAnWmGNYYWVuf9gamQYG4IawBCNTITHq5Mz8urbqyQq311cunPgCIPsIagECdmUmrs7FGiQoa4q5XV3NSI8W1fgCij7AGIFAjqQV2gm5Qd3Pt8vQxgOgjrAEI1JmZtLrZXLAh3c1JpkGBGCGsAQiMc47TCzahqzmp6fklLWRyQZcCYBsQ1gAEJpXOaj6TYyfoBnl/X2dYtwbEAmENQGDO91gjrG2EN208wro1IBYIawACw+kFm3N+ZI2wBsQBYQ1AYLyRoc4mwtpGdDENCsQKYQ1AYM7MpGUmdTQS1jYiWZXQjroqRtaAmCCsAQjMyExabQ01qq7kq2ijuptrWbMGxATfkAACMzyzoB7Wq21Kd3OSkTUgJghrAAIzNL2g3h00xN2MLhrjArFBWAMQCOechqcX1MPpBZvS3ZzU5FxG6SUa4wJRR1gDEIiJuYzSS3lG1japi15rQGwQ1gAEYni60Haip4Wwthk99FoDYoOwBiAQQ1OFsNZLWNsUr9faSIpea0DUEdYABGKoOLLWxzTopnQxsgbEBmENQCCGphdUV51Qc21V0KWEUl11pZprq3RmmrAGRB1hDUAghqYW1NtSKzMLupTQotcaEA+ENQCBGJ6hx9pWdTcnWbMGxABhDUAghqYW2Am6RV0cOQXEAmENwLabz2Q1Nb/ETtAt6m5O6uy5jBazNMYFooywBmDbeT3WCGtb013cETo6sxhwJQD8RFgDsO0GvR5rrFnbku7iKQZnZli3BkQZYQ3AthsutptgZG1rzjfGZd0aEGWENQDbbmh6XokKU0djTdClhFo3jXGBWCCsAdh2Q1ML6mpKqjLBV9BW1NdUqilZqTPTTIMCUcY3JYBtNzydZr1aiXQ31zKyBkQcYQ3AthuaXmC9Wol0NSdZswZEnK9hzcxuM7OjZnbczD66xuu3mNn3zSxrZu9Z9VrOzJ4q/nnQzzoBbJ9sLq+RVJqwViIcOQVEX6Vfb2xmCUn3SnqbpEFJj5vZg865IysuOy3ppyT90hpvseCcu96v+gAEY3R2Ubm84/SCEulurtXZc4vKZPOqrmSyBIgiP//LvknScefcCedcRtIDku5YeYFz7pRz7hlJeR/rAFBGhuixVlLdzUk5J40yFQpElp9hrVfSwIrHg8Xn1itpZofM7BEze3dpSwMQFE4vKC1vhHKYHaFAZPk2DSrJ1njObeD+Xc65YTPbK+kbZvasc+6lV3yA2V2S7pKkXbt2bb5SANtmqBgqelqSAVcSDd3Fv8dhTjEAIsvPkbVBSf0rHvdJGl7vzc654eI/T0j6lqQb1rjmPufcQefcwfb29q1VC2BbDE0vaGd9teqq/fxdMT56mr2RNaZBgajyM6w9Lmmfme0xs2pJd0pa165OM9thZjXFn9skvVHSkYvfBSAMhqZo21FKtdUJ7airYhoUiDDfwppzLivpbkkPS3pe0hecc4fN7B4zu12SzOxGMxuU9BOSPm1mh4u3v0bSITN7WtI3JX1y1S5SACE1NL3AFGiJ9bTQGBeIMl/nIZxzD0l6aNVzH1vx8+MqTI+uvu+7kl7rZ20Atp9zTsPTC7plH8sWSqm7uVaDU/NBlwHAJzTlAbBtpueXNJ/JMbJWYr0tSaZBgQgjrAHYNt5O0D56rJVUd0utUumszi1mgy4FgA8IawC2zdByj7W6gCuJFq/X2hlG14BIIqwB2Dbe6QVMg5ZWT3Ph73OIsAZEEmENwLYZnl5QsqpCO+urgy4lUpZH1tgRCkQSYQ3AthmaLvRYM1vrgBNsVkdjjSqMI6eAqCKsAdg2hR5rbC4otcpEhbqakpxiAEQUYQ3AthmeXmAnqE+6W2oZWQMiirAGYFukl3I6ey6zfJYlSqtwigFhDYgiwhqAbeGN+vQysuaLnuakhmfScs4FXQqAEiOsAdgW53usEdb80NNSq0w2r4m5TNClACgxwhqAbXG+xxphzQ/dxV5rrFsDooewBmBbDE8vqMKkrmYa4vrBC8HsCAWih7AGYFsMTi+oqympqgRfO344H9YYWQOihm9NANtimB5rvtpRV6VkVQU7QoEIIqwB2BZD0wvsBPWRmamnuZZpUCCCCGsAfJfLO52ZTjOy5rOelloNM7IGRA5hDYDvxmcXlc072nb4rLs5yZo1IIIIawB8NzQ9L4kea37raanV2OyilnL5oEsBUEKENQC+Gyz2WONcUH/1tCTlnDQyw7o1IEoIawB8NzBZGFnr21EXcCXRRvsOIJoIawB8Nzi1oLaGGtVWJ4IuJdK6mwth7Qwja0CkENYA+G5gap4p0G3Q01I4HWKIkTUgUghrAHw3MLmg/p1MgfqtrrpSLXVVNMYFIoawBsBXubzT8PSC+hlZ2xY0xgWih7AGwFcjqbSyecfmgm3S00KvNSBqCGsAfOXtBO3fycjaduhpqSWsARFDWAPgK6/HWj8ja9uiu7lWqXRW5xazQZcCoEQIawB8NTA5LzNxLug2Wd4ROsXoGhAVhDUAvhqYmldXU1LVlXzdbIddxV233vQzgPDj2xOArwanFpgC3UZeWDtNWAMig7AGwFeDk/PqY3PBttlZX6366gRhDYgQwhoA32SyeY2k0rTt2EZmpv6ddUyDAhFCWAPgmzMzC8o70RB3m+3aWcfIGhAhhDUAvhmYLOxIZGRte3lhzTkXdCkASoCwBsA3L0/OSZJ2txHWttOu1jotZvMan10MuhQAJUBYA+CbU2fnVFNZoc7GZNClxEo/O0KBSCGsAfDNqYl5XdZap4oKC7qUWKF9BxAthDUAvnl5Yk6XtdYHXUbs9LbUyoywBkQFYQ2AL/J5p5cn5rWnjbC23ZJVCXU1JQlrQEQQ1gD4YnQ2rcVsXpe1srkgCPRaA6KDsAbAFyfPFneCMg0aCHqtAdFBWAPgi5cnCkGBkbVg9O+o02hqUemlXNClANgiwhoAX5yamFN1okLdzZxeEIRdrYW/d6ZCgfAjrAHwxctn59W/s1YJ2nYEYk9bgyTpRHE6GkB4EdYA+OLUxBw7QQO0t73wd39inLAGhB1hDUDJOed0ih5rgWpKVqmtoUYnxs8FXQqALSKsASi5sdlFpZfy2s3mgkDtba9nGhSIAMIagJI7VQwIjKwF6/L2+uUWKgDCi7AGoOS8gMCatWDtbWvQ5FxG0/OZoEsBsAWENQAld+LsnKorK9TTQtuOIHmbDF5ikwEQaoQ1ACV3Yvyc9rTW07YjYHvbi+072GQAhBphDUDJvTQ+tzyqg+D076hVVcLYZACEnK9hzcxuM7OjZnbczD66xuu3mNn3zSxrZu9Z9doHzezF4p8P+lkngNLJZPM6PTlPWCsDlYkK7dpZx8gaEHK+hTUzS0i6V9I7JB2Q9D4zO7DqstOSfkrSZ1fdu1PSxyXdLOkmSR83sx1+1QqgdE5PziuXd9pb7KCPYO1tb6AxLhByfo6s3STpuHPuhHMuI+kBSXesvMA5d8o594yk/Kp7b5X0VefcpHNuStJXJd3mY60ASsQbxWFkrTzsba/XyxOFAA0gnPwMa72SBlY8Hiw+5/e9AALkrY/yFrcjWJe3NSiTy2twigPdgbDyM6yttQ1svb/areteM7vLzA6Z2aHx8fENFQfAHyfGz6mtoVrNtVVBlwJJl3cURjiPj7FuDQgrP8PaoKT+FY/7JA2X8l7n3H3OuYPOuYPt7e2bLhRA6ZwYn2O9Whm5oqNRkvQiYQ0ILT/D2uOS9pnZHjOrlnSnpAfXee/Dkt5uZjuKGwveXnwOQJk7cZa2HeWkubZKnU01enGUsAaElW9hzTmXlXS3CiHreUlfcM4dNrN7zOx2STKzG81sUNJPSPq0mR0u3jsp6TdVCHyPS7qn+ByAMjY1l9HkXIawVmb2dTTqxbHZoMsAsEmVfr65c+4hSQ+teu5jK35+XIUpzrXuvV/S/X7WB6C0TpwtjN5czuaCsrKvs0Gff3xA+bxTBadKAKHDCQYASsY7g5KdoOVlX0ej5jM5Dc8sBF0KgE0grAEomRPjc6pKmPp3cIB7OdnXWQjPrFsDwomwBqBkToyf066ddapM8NVSTvZ1FMMa69aAUOIbFUDJFHaCMgVablrqqtXeyI5QIKwIawBKIpPN69TZOV3RQVgrR/s6GnSMXmtAKBHWAJTEqYk5ZfNOV3YS1srRvo4GHR+dlXOcEQqEDWENQEkcGy2sh9pX7JiP8rKvs1FzmZzOzKSDLgXABhHWAJTEsdFzqjAxDVqmvE0GXqgGEB6ENQAl8eLorHbtrFOyKhF0KVjDvs7CiCcHugPhQ1gDUBLHRmeXAwHKz876arU1VLMjFAghwhqALVvM5nRqYp7NBWXuio4GHaPXGhA6hDUAW3bq7LxyeacrGVkra/s6GnV89Bw7QoGQIawB2DJ2gobDlZ0Nml3MajS1GHQpADaAsAZgy14cnVWFSXvb64MuBRdxRTFMsyMUCBfCGoAtOzZ6Trtb69kJWuaWD3RnRygQKoQ1AFt2bGx2OQigfLU11GhnfbWOs8kACBXCGoAtWcjkdOrsnK7qagq6FKzDFR0NOjpCWAPChLAGYEteGEkp76QDPYS1MNjf2ahj7AgFQoWwBmBLjpxJSZIOdBPWwuCq7kadW8xqcGoh6FIArBNhDcCWHB5OqSlZqb4dtUGXgnW4qquwI5SpUCA8CGsAtuTIcEoHeppkZkGXgnXwGhcfpX0HEBqENQCblss7vTCS0oHu5qBLwTo1JqvU21KrFxhZA0KDsAZg006ePaf0Ul5Xs7kgVK7qatTRkVTQZQBYJ8IagE07PFzcXEBYC5X9XY06MT6nTDYfdCkA1oGwBmDTjpxJqTpRoSs6aIgbJvu7GpXNO700zkkGQBgQ1gBs2pHhlK7salBVgq+SMHlNsc0KO0KBcOAbFsCmOOcKO0HprxY6e9rqVZUwNhkAIUFYA7ApY7OLmpjLENZCqCpRocvbG9hkAIQEYQ3AphwenpEkXd1L244wuqqrkZE1ICQIawA25UhxJ6jXER/hsr+rSWdm0pqZXwq6FACXQFgDsClHzqR0WWudGpNVQZeCTVg+doqTDICyR1gDsCmHh1M0ww2x/ctnhLJuDSh3hDUAGzabXtLLE/NsLgix7uakmpKVrFsDQoCwBmDDvP/Bc3JBeJmZrupqIqwBIUBYA7Bhh4cKO0E5wD3cDvQ06fkzKeXzLuhSAFwEYQ3Ahh05k1JrfbU6m2qCLgVbcHVPk+YzOZ2cmAu6FAAXQVgDsGFHzqR0oKdJZhZ0KdiCa4o98p4rjpQCKE+ENQAbspTL69jIOTYXRMC+jgbVVFYQ1oAyR1gDsCHHx84pk8uzuSACKhMVuqq7Sc8N0b4DKGeENQAb4p1cQI+1aLimp0nPDc/IOTYZAOWKsAZgQ46cSSlZVaE9bQ1Bl4ISuKa3WbPprAYmF4IuBcAFENYAbMjh4Rld1dWkRAWbC6Lgmp7iJoNh1q0B5YqwBmDdnHM6MpxivVqEXNnVoMoKY5MBUMYIawDWbWh6Qal0lp2gEVJTmdCVnY16bphNBkC5IqwBWLfDbC6IpGt6m/TcEJsMgHJFWAOwbkeGU6ow6aouwlqUXNPbrMm5jM7MpIMuBcAaCGsA1u3ImZT2tNWrtjoRdCkooauLmwyeZd0aUJYIawDW7chwavl/7IiOq3uaVFlhenpgOuhSAKyBsAZgXSbnMhqaXmAnaAQlqxI60NOk75+eCroUAGsgrAFYF2+K7No+Rtai6Ib+Fj0zOKNsLh90KQBWIawBWJdnBwtTZNf0Etai6HWX7dB8Jqdjo+eCLgXAKoQ1AOvyzOCM9rbVqylZFXQp8MEN/TskSU8OMBUKlBvCGoB1eWZwhinQCOvfWavW+mo9eZpNBkC58TWsmdltZnbUzI6b2UfXeL3GzD5ffP1RM9tdfH63mS2Y2VPFP3/qZ50ALm4sldZIKq3X9rUEXQp8Yma6YVeLnmSTAVB2fAtrZpaQdK+kd0g6IOl9ZnZg1WU/K2nKOXeFpP8h6b+veO0l59z1xT8f8qtOAJfG5oJ4uGHXDr00PqeZ+aWgSwGwgp8jazdJOu6cO+Gcy0h6QNIdq665Q9Jnij//jaS3mJn5WBOATXh6YFoVJs4Ejbgb+gsjp08NMhUKlBM/w1qvpIEVjweLz615jXMuK2lGUmvxtT1m9qSZfdvM3rTWB5jZXWZ2yMwOjY+Pl7Z6AMsOvTyl13Q3qb6mMuhS4KNr+1tkJqZCgTLjZ1hba4Rs9SnBF7rmjKRdzrkbJH1E0mfN7FW/0jvn7nPOHXTOHWxvb99ywQBebSmX15Onp3Xj7p1BlwKfNdRUan9nI5sMgDLjZ1gblNS/4nGfpOELXWNmlZKaJU065xadcxOS5Jx7QtJLkq70sVYAF3B4OKWFpRxhLSZu2LVD3z89pVx+9e/WAILiZ1h7XNI+M9tjZtWS7pT04KprHpT0weLP75H0DeecM7P24gYFmdleSfsknfCxVgAXcOjUpCTpxt07Aq4E2+HmPTs1m87q+TOpoEsBUORbWCuuQbtb0sOSnpf0BefcYTO7x8xuL172/0lqNbPjKkx3eu09bpH0jJk9rcLGgw855yb9qhXAhT12clKXtdapoykZdCnYBjfvLYygPnJiIuBKAHh8XS3snHtI0kOrnvvYip/Tkn5ijfu+KOmLftYG4NKcczr08pR+ZH9H0KVgm3Q312rXzjo9enJSP/emvUGXA0CcYADgIl4YmdXkXGZ5tAXxcPOenXr81KTyrFsDygJhDcAFfftYoSXOLfvYbR0nN+9t1fT8ko6OzgZdCgAR1gBcxD8fG9f+zkZ1NbNeLU5u3lMYSX2UdWtAWSCsAVjTfCarQ6emdMuVbUGXgm3Wv7NOvS21evQk+7qAckBYA7CmR05MKJPL681Xsrkgjm7eu1OPnJhg3RpQBghrANb0raPjSlZV6CD91WLpTfvaNDW/pOeGZ4IuBYg9whqAV8nnnf7p8KjefGW7klWJoMtBAN5U3FTyz8c4dxkIGmENwKs8PTitkVRat17dFXQpCEhbQ42u6W3SPx87G3QpQOwR1gC8ysOHR1VZYXrLVZ1Bl4IA3bKvXU+cnlIqvRR0KUCsEdYAvIJzTg8fHtEbLm9Vc11V0OUgQLdc2a5c3um7x2nhAQSJsAbgFV4cO6eTZ+f0dqZAY+/1l+1QY7JSX3t+NOhSgFgjrAF4ha88NyIz6dYDTIHGXVWiQm+5qkNff35U2Vw+6HKA2CKsAXiFhw+P6Ib+FnU0cWoBpFuv7tLU/JIeO0WDXCAohDUAywYm53V4OMUuUCx78/521VRW6J8OMxUKBIWwBmDZw4dHJImwhmV11ZV60752PXx4hNMMgIAQ1gAse+jZM7qqq1G72+qDLgVl5Eev69aZmbQeZyoUCARhDYCkwhTo909P6/bre4IuBWXmbQc6VVed0N89ORR0KUAsEdYASJL+8ZkzkqQfvZawhleqq67UbVd36f8+e0bppVzQ5QCxQ1gDIEn60tPDur6/Rf0764IuBWXox17Xq9l0Vt94YSzoUoDYIawB0PGxczpyJqXbr2NUDWv7wcvb1NFYw1QoEADCGgB96elhmUnvurY76FJQphIVpjuu79E3XxjT2XOLQZcDxAphDYi5fN7pi98f1Bv2tqqTRri4iPfe2K9s3ulvnhgMuhQgVghrQMw9cmJCg1MLeu+N/UGXgjJ3RUejbtq9Uw88dpqea8A2IqwBMff5QwNqSlbSCBfr8r6b+3VqYl7fOzERdClAbBDWgBibns/oy8+N6N039CpZlQi6HITAO67pVnNtlT772OmgSwFig7AGxNjnHhtQJpvX+27aFXQpCIlkVUL/7nV9+qfDIxpNpYMuB4gFwhoQU0u5vD7z3VP6wctb9ZrupqDLQYh84A2XKZt3+vPvnQq6FCAWCGtATD307BmNpNL62R/aE3QpCJndbfV6+4FO/eUjpzWfyQZdDhB5hDUghpxzuv87J7W3rV4/sr8j6HIQQj//pr2aWVjSFx4fCLoUIPIIa0AMPXZyUk8Pzuin37hbFRUWdDkIoddftkM37t6hP/n2S5wXCviMsAbE0P/6xnG1NdToJw7SWw2bY2b6yNv2azS1qL96lJ2hgJ8Ia0DMPPHypL5z/Kx+4Za9tOvAlrzh8la98YpW/fE3j2s2vRR0OUBkEdaAmPnDrx/Xzvpq/eQP0K4DW/crt12lyfmM/vDrLwZdChBZhDUgRp4amNa3j43r5960R3XVlUGXgwi4tq9F7z3Yrz/711M6PjYbdDlAJBHWgBj5n187ppa6Kn3gDbuDLgUR8su37ldddUIff/CwnOPMUKDUCGtATHz3+Fl96+i4PvTmy9VQw6gaSqe1oUb/9e379a/HJ/Tg08NBlwNEDmENiIF83ul3vvy8eltq9VM/uDvochBB7/+By3RdX7Pu+dIRTc9ngi4HiBTCGhADDz49rOeGUvqlW69kByh8kagw/e6PX6vphSX9zkPPB10OECmENSDiZhaW9Ltffl7X9Dbpjut6gy4HEXagp0k//6a9+sKhQX33pbNBlwNEBmENiLjf/r9HdPZcRr/7Y9dyWgF894tv2addO+v0a3/3HCcbACVCWAMi7OHDI/rCoUHddctevbavOehyEAO11Qn9zo+9VifPzunebx4PuhwgEghrQEQdHZnVRz7/lK7ra9YvvmVf0OUgRn5oX5t+/HW9+pNvvaSjI/ReA7aKsAZE0OmJef30nz2muppKffo/HmRTAbbdr7/rgBqTlfrVv31G+Ty914CtIKwBEXN87Jzee9/3NL+U05/91I3qak4GXRJiaGd9tT72owf0/dPT+gOOogK2hLAGRMi3j43rx/74X5XJ5vVXP3ezrullnRqC8+7re/We1/fpD77+or7+/GjQ5QChRVgDIsA5p/u/c1I//WePqbelVv9w9xt1dQ9BDcEyM/3Wu6/RNb1N+vBnv6/vvTQRdElAKBHWgO6qBkcAAAv3SURBVJA7t5jV3Z97Uvf84xG95TWd+uJ/+kH17agLuixAkpSsSuj//PRN6t9Rp5/5P4/rnw6PBF0SEDqENSDEnhmc1u3/6zv6ynMj+pXbrtKn3/961XPuJ8pMW0ONPvvzP6B9nQ266y+e0O89/IIWs/RgA9aLsAaEUCq9pHu+dETvvvdfNZfJ6rM/d7P+0w9fTtNblK32xhp94RfeoPce7Ne933xJ7/rD7+jRE0yLAuvBr+BAiEzOZXT/d07qM987pXOLWb3/5sv0y7ftV1OyKujSgEtKViX0399zrd7x2i792t89p/fe94h+ZH+7funW/ayxBC6CsAaEwMhMWv/vv5zQZx89rXQ2p9uu7tKHf+QKdnsilH54f4e++pFb9Jnvvqw//XZhlO1N+9r0gTf8/+3de4wdZRnH8e/v7LX0sq0FetlSLqVqQAzQFTAgVAEDhNCgRFYTJUqsEFFJNFG8UeEfUdFAwAsCiRAUlevGiFzEKEZASgGlgGmRCktLuZRuW3rZPXse/5jZdnt6TneU7s50z++TnOxc3jPnybvvzHnOvPPOHMSH3r0/TT5DbLYTJ2tmBfbC62/xsz8/z+3LeqkELDpyNheeNI/5MybnHZrZ27JPazMXLpzHJ46dy01/W8Utj77IZ29aSufUCZyzYA4fObqTA6dPzDtMs0JwsmZWQE+8+CbXP/QC9zy9huamEt3vm8viEw/hgHd4lKeNLx0TWvjCyfO5YOE8HnhmLbc8+iJXP7iCq/64ggUHTuPsozo5872zmLpPa96hmuVmVJM1SacBVwFNwPUR8d2q9W3ATcAC4A3g3IhYla67BDgfGAS+GBH3jmasZnmICDZtK/Paxm38543NPPHSeu5b/grPvbKRye3NLD5xHp854SD2n+ynENj41tJU4vQjZnH6EbNY07eFu55YzR3LevnmXU/z7buf5ojODo6bN533dk5l/oxJHDR9Iq3NHiNnjWHUkjVJTcC1wKlAL/CYpJ6IeGZYsfOBNyPiUEndwBXAuZIOA7qBw4HZwAOS3hkRHutthVWpBAOVCgODQXmwwvrNA7yyYStrN2zllb6tvLZxG+s297PureT1xqZ+Xt+0jW3lyvZtSNB14DS+c9bhfHTBHCb5NhzWgGZ1TODChfO44KRDWL56A/c9s5aHn3+dG//6AgODyXNGm0pi5pR2Zk9tZ1bHBGZ1tDNjSjvTJrYwdUIrHfu00DGhhSntLbS1lGhtSl4eMW17o9H8JjgGWBkR/waQdCuwCBierC0ClqTTtwHXSFK6/NaI2Aa8IGllur2HRzHeEX3lt0+xpX9Hvhjs+nDiqPG84uplWd5X67HHtbZdXbLm59fcVmQoM/K2qrdTz/9TB2/rfSMuyP5/KFeCgXKFgcGhV+w03T9YoTxYYaRnVbe3lJg+sY13TGxl2sRW5u03iX0ntbLf5Db2ndRG59QJHDZ7CpM9stMMSJ6A8J7OjmQgzanvZOvAIM+/tomVr25ixdpNvLx+C2v6tvBU73r+sHwr/cN++NTTXBKtzSWaS6KlqURzk2gulWhpGppPpptLGjZdoiQoSUgAyd+SQNunBc4Dx42ZU9r51pmH5R3GdqOZrHUCLw2b7wWOrVcmIsqS+oDp6fJHqt7bWf0BkhYDiwHmzp27xwKvZ8XajbzVv/PJvVr7pmosVFXJWmV23c6uhbJ8XpbPr/m+2kGMGEPtz6u1KWUoU2tbIwe6S0zV21KtOlDtz6talhzIdxzMW5pKtDanB/adDvJDy5KDfMeEFmZOaWdmRxszprQzqa255v/UiufSky4FYMmf0vkcY7Ed2luaOHx2R83bfEQE6zcPsH7LAOs397N+ywB9mwfYsHWA/nKF/sEK/emPruRvUK5UGCgnZ8TLQ/PpmfGhH2VbByqUB8tUIvmBV6kkP+KGfqhWIohI/tr4saW/WB15o5ms1fpWqm7N9cpkeS8RcR1wHUBXV9eo7yl3X3TCaH+EmRXAkoVL8g7B/keSmJaetQaPIrXxZTSvzuwFDhg2PwdYXa+MpGagA1iX8b1mZmZm495oJmuPAfMlHSyplWTAQE9VmR7gvHT6HODBSM4t9wDdktokHQzMB/4+irGamZmZFdKodYOm16BdBNxLcuuOGyNiuaTLgKUR0QPcANycDiBYR5LQkZb7DclghDLweY8ENTMzs0akrKP5iq6rqyuWLl2adxhmZmZmI5L0eER0ZSnrOwqamZmZFZiTNTMzM7MCc7JmZmZmVmBO1szMzMwKzMmamZmZWYE5WTMzMzMrMCdrZmZmZgXmZM3MzMyswJysmZmZmRWYkzUzMzOzAnOyZmZmZlZgTtbMzMzMCszJmpmZmVmBOVkzMzMzKzAna2ZmZmYF5mTNzMzMrMCcrJmZmZkVmJM1MzMzswJzsmZmZmZWYIqIvGPYIyS9Bvwn7zj2sH2B1/MOYi/husrOdZWd6yo711V2rqvsxnNdHRgR+2UpOG6StfFI0tKI6Mo7jr2B6yo711V2rqvsXFfZua6yc10l3A1qZmZmVmBO1szMzMwKzMlasV2XdwB7EddVdq6r7FxX2bmusnNdZee6wtesmZmZmRWaz6yZmZmZFZiTtQKR9GtJT6avVZKerFNulaR/puWWjnWcRSBpiaSXh9XXGXXKnSbpX5JWSvraWMdZBJK+L+k5Sf+QdKekqXXKNWy7GqmdSGpL98+Vkh6VdNDYR5k/SQdI+pOkZyUtl/SlGmUWSuobtm9+O49Yi2CkfUqJq9N29Q9JR+cRZ94kvWtYe3lS0gZJF1eVaeh21Zx3ALZDRJw7NC3pSqBvN8U/GBHj9d4zWf0oIn5Qb6WkJuBa4FSgF3hMUk9EPDNWARbE/cAlEVGWdAVwCfDVOmUbrl1lbCfnA29GxKGSuoErgHN33dq4Vwa+HBHLJE0GHpd0f4196qGIODOH+Ipod/vU6cD89HUs8JP0b0OJiH8BR8L2/fFl4M4aRRu2XfnMWgFJEvAx4Fd5x7KXOwZYGRH/joh+4FZgUc4xjbmIuC8iyunsI8CcPOMpoCztZBHwi3T6NuDkdD9tKBGxJiKWpdMbgWeBznyj2qstAm6KxCPAVEmz8g4qZycDz0fEeLvJ/dviZK2YPgCsjYgVddYHcJ+kxyUtHsO4iuaitOvgRknTaqzvBF4aNt+Lv1g+A9xTZ12jtqss7WR7mTTx7QOmj0l0BZV2BR8FPFpj9fslPSXpHkmHj2lgxTLSPuVj1K66qX+iomHblbtBx5ikB4CZNVZ9IyLuTqc/zu7Pqh0fEasl7Q/cL+m5iPjLno41b7urK5LugstJDoaXA1eSJCI7baLGe8fl8Ocs7UrSN0i6sW6ps5mGaFc1ZGknDdOWspA0CbgduDgiNlStXkbyGJ1N6bWkd5F08zWikfYpt6thJLUCZ5FcqlGtoduVk7UxFhGn7G69pGbgI8CC3Wxjdfr3VUl3knTjjLsv1ZHqaoiknwO/q7GqFzhg2PwcYPUeCK1wMrSr84AzgZOjzv16GqVd1ZClnQyV6U330Q5g3diEVyySWkgStVsi4o7q9cOTt4j4vaQfS9q30a6FhEz7VMMcozI6HVgWEWurVzR6u3I3aPGcAjwXEb21VkqamF7Yi6SJwIeBp8cwvkKouq7jbGrXwWPAfEkHp7/YuoGesYivSCSdRjKg4KyI2FynTCO3qyztpAc4L50+B3iwXtI7nqXX6d0APBsRP6xTZubQ9XySjiH5nnlj7KIshoz7VA/wqXRU6HFAX0SsGeNQi6Rur1KjtyufWSueXfrrJc0Gro+IM4AZwJ1pm20GfhkRfxjzKPP3PUlHknQZrAI+BzvXVTr68SLgXqAJuDEilucVcI6uAdpIumEAHomIC9yuEvXaiaTLgKUR0UOSoNwsaSXJGbXu/CLO1fHAJ4F/asethb4OzAWIiJ+SJLMXSioDW4DuRkxsqbNPSboAttfV74EzgJXAZuDTOcWaO0n7kIzI/tywZcPrqqHblZ9gYGZmZlZg7gY1MzMzKzAna2ZmZmYF5mTNzMzMrMCcrJmZmZkVmJM1MzMzswJzsmZmZmZWYE7WzMzMzArMyZqZmZlZgf0XUf9Atq5K/BUAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the plot above the mean and median are both so close to zero that the red median line lies on top of the thicker black line drawn at the mean.\n",
        "\n",
        "In skewed distributions, the mean tends to get pulled in the direction of the skew, while the median tends to resist the effects of skew:"
      ],
      "metadata": {
        "id": "jQAp8WUe3nZI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "skewed_data = pd.DataFrame(np.random.exponential(size=100000))\n",
        "\n",
        "skewed_data.plot(kind=\"density\",\n",
        "              figsize=(10,10),\n",
        "              xlim=(-1,5));\n",
        "\n",
        "\n",
        "plt.vlines(skewed_data.mean(),     # Plot black line at mean\n",
        "           ymin=0,\n",
        "           ymax=0.8,\n",
        "           linewidth=5.0);\n",
        "\n",
        "plt.vlines(skewed_data.median(),   # Plot red line at median\n",
        "           ymin=0,\n",
        "           ymax=0.8,\n",
        "           linewidth=2.0,\n",
        "           color=\"red\");"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:34.140740Z",
          "iopub.execute_input": "2024-09-03T12:01:34.141158Z",
          "iopub.status.idle": "2024-09-03T12:01:43.478029Z",
          "shell.execute_reply.started": "2024-09-03T12:01:34.141084Z",
          "shell.execute_reply": "2024-09-03T12:01:43.476926Z"
        },
        "trusted": true,
        "id": "sW6rumbw3nZI",
        "outputId": "968d08e7-b830-45ce-ea81-e412c4429457"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 720x720 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The mean is also influenced heavily by outliers, while the median resists the influence of outliers:"
      ],
      "metadata": {
        "id": "dJ7hvJoy3nZI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "norm_data = np.random.normal(size=50)\n",
        "outliers = np.random.normal(15, size=3)\n",
        "\n",
        "combined_data = pd.DataFrame(np.concatenate((norm_data, outliers), axis=0))\n",
        "\n",
        "combined_data.plot(kind=\"density\",\n",
        "              figsize=(10,10),\n",
        "              xlim=(-5,20));\n",
        "\n",
        "\n",
        "plt.vlines(combined_data.mean(),     # Plot black line at mean\n",
        "           ymin=0,\n",
        "           ymax=0.2,\n",
        "           linewidth=5.0);\n",
        "\n",
        "plt.vlines(combined_data.median(),   # Plot red line at median\n",
        "           ymin=0,\n",
        "           ymax=0.2,\n",
        "           linewidth=2.0,\n",
        "           color=\"red\");"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:43.480056Z",
          "iopub.execute_input": "2024-09-03T12:01:43.480519Z",
          "iopub.status.idle": "2024-09-03T12:01:43.800692Z",
          "shell.execute_reply.started": "2024-09-03T12:01:43.480431Z",
          "shell.execute_reply": "2024-09-03T12:01:43.799583Z"
        },
        "trusted": true,
        "id": "wlXMjWY03nZI",
        "outputId": "f1298c7e-a4d9-43f7-e2f8-70c40aef522c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 720x720 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since the median tends to resist the effects of skewness and outliers, it is known a \"robust\" statistic. The median generally gives a better sense of the typical value in a distribution with significant skew or outliers.\n",
        "\n",
        "The mode of a variable is simply the value that appears most frequently. Unlike mean and median, you can take the mode of a categorical variable and it is possible to have multiple modes. Find the mode with df.mode():"
      ],
      "metadata": {
        "id": "e-v1XU5n3nZJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars.mode()"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:43.802358Z",
          "iopub.execute_input": "2024-09-03T12:01:43.802798Z",
          "iopub.status.idle": "2024-09-03T12:01:43.841047Z",
          "shell.execute_reply.started": "2024-09-03T12:01:43.802725Z",
          "shell.execute_reply": "2024-09-03T12:01:43.839886Z"
        },
        "trusted": true,
        "id": "Kz7SVuUt3nZJ",
        "outputId": "d0d0a355-a1f4-4737-ebbf-f17e5ba37d4b"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 9,
          "output_type": "execute_result",
          "data": {
            "text/plain": "    mpg  cyl   disp     hp  drat    wt   qsec   vs   am  gear  carb\n0  10.4  8.0  275.8  110.0  3.07  3.44  17.02  0.0  0.0   3.0   2.0\n1  15.2  NaN    NaN  175.0  3.92   NaN  18.90  NaN  NaN   NaN   4.0\n2  19.2  NaN    NaN  180.0   NaN   NaN    NaN  NaN  NaN   NaN   NaN\n3  21.0  NaN    NaN    NaN   NaN   NaN    NaN  NaN  NaN   NaN   NaN\n4  21.4  NaN    NaN    NaN   NaN   NaN    NaN  NaN  NaN   NaN   NaN\n5  22.8  NaN    NaN    NaN   NaN   NaN    NaN  NaN  NaN   NaN   NaN\n6  30.4  NaN    NaN    NaN   NaN   NaN    NaN  NaN  NaN   NaN   NaN",
            "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>mpg</th>\n      <th>cyl</th>\n      <th>disp</th>\n      <th>hp</th>\n      <th>drat</th>\n      <th>wt</th>\n      <th>qsec</th>\n      <th>vs</th>\n      <th>am</th>\n      <th>gear</th>\n      <th>carb</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <td>0</td>\n      <td>10.4</td>\n      <td>8.0</td>\n      <td>275.8</td>\n      <td>110.0</td>\n      <td>3.07</td>\n      <td>3.44</td>\n      <td>17.02</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>3.0</td>\n      <td>2.0</td>\n    </tr>\n    <tr>\n      <td>1</td>\n      <td>15.2</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>175.0</td>\n      <td>3.92</td>\n      <td>NaN</td>\n      <td>18.90</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>4.0</td>\n    </tr>\n    <tr>\n      <td>2</td>\n      <td>19.2</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>180.0</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n    </tr>\n    <tr>\n      <td>3</td>\n      <td>21.0</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n    </tr>\n    <tr>\n      <td>4</td>\n      <td>21.4</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n    </tr>\n    <tr>\n      <td>5</td>\n      <td>22.8</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n    </tr>\n    <tr>\n      <td>6</td>\n      <td>30.4</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The columns with multiple modes (multiple values with the same count) return multiple values as the mode. Columns with no mode (no value that appears more than once) return NaN."
      ],
      "metadata": {
        "id": "CJ_z2Qmy3nZJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Measures of Spread"
      ],
      "metadata": {
        "id": "8xbqvSMD3nZJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Measures of spread (dispersion) are statistics that describe how data varies. While measures of center give us an idea of the typical value, measures of spread give us a sense of how much the data tends to diverge from the typical value.\n",
        "\n",
        "One of the simplest measures of spread is the range. Range is the distance between the maximum and minimum observations:"
      ],
      "metadata": {
        "id": "pOKqIwhs3nZJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "max(mtcars[\"mpg\"]) - min(mtcars[\"mpg\"])"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:43.842821Z",
          "iopub.execute_input": "2024-09-03T12:01:43.843219Z",
          "iopub.status.idle": "2024-09-03T12:01:43.851240Z",
          "shell.execute_reply.started": "2024-09-03T12:01:43.843153Z",
          "shell.execute_reply": "2024-09-03T12:01:43.849708Z"
        },
        "trusted": true,
        "id": "1vO0NgR33nZK",
        "outputId": "3db66df2-9ca8-4f7b-9dd6-7322d9d2a6ec"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 10,
          "output_type": "execute_result",
          "data": {
            "text/plain": "23.5"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As noted earlier, the median represents the 50th percentile of a data set. A summary of several percentiles can be used to describe a variable's spread. We can extract the minimum value (0th percentile), first quartile (25th percentile), median, third quartile(75th percentile) and maximum value (100th percentile) using the quantile() function:"
      ],
      "metadata": {
        "id": "Zfq2nK-z3nZK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "five_num = [mtcars[\"mpg\"].quantile(0),\n",
        "            mtcars[\"mpg\"].quantile(0.25),\n",
        "            mtcars[\"mpg\"].quantile(0.50),\n",
        "            mtcars[\"mpg\"].quantile(0.75),\n",
        "            mtcars[\"mpg\"].quantile(1)]\n",
        "\n",
        "five_num"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:43.853051Z",
          "iopub.execute_input": "2024-09-03T12:01:43.853492Z",
          "iopub.status.idle": "2024-09-03T12:01:43.875486Z",
          "shell.execute_reply.started": "2024-09-03T12:01:43.853419Z",
          "shell.execute_reply": "2024-09-03T12:01:43.874187Z"
        },
        "trusted": true,
        "id": "wFXr_Mux3nZK",
        "outputId": "70f735bf-b48c-472e-b04f-05861c090781"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 11,
          "output_type": "execute_result",
          "data": {
            "text/plain": "[10.4, 15.425, 19.2, 22.8, 33.9]"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since these values are so commonly used to describe data, they are known as the \"five number summary\". They are the same percentile values returned by df.describe():"
      ],
      "metadata": {
        "id": "2s9mAQOq3nZK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars[\"mpg\"].describe()"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:43.876929Z",
          "iopub.execute_input": "2024-09-03T12:01:43.877257Z",
          "iopub.status.idle": "2024-09-03T12:01:43.891909Z",
          "shell.execute_reply.started": "2024-09-03T12:01:43.877196Z",
          "shell.execute_reply": "2024-09-03T12:01:43.890763Z"
        },
        "trusted": true,
        "id": "Y1fg-Cjb3nZK",
        "outputId": "5bf6575c-f12f-423d-b5eb-6f882b920d85"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 12,
          "output_type": "execute_result",
          "data": {
            "text/plain": "count    32.000000\nmean     20.090625\nstd       6.026948\nmin      10.400000\n25%      15.425000\n50%      19.200000\n75%      22.800000\nmax      33.900000\nName: mpg, dtype: float64"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Interquartile (IQR) range is another common measure of spread. IQR is the distance between the 3rd quartile and the 1st quartile:"
      ],
      "metadata": {
        "id": "M9aO7OXX3nZL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars[\"mpg\"].quantile(0.75) - mtcars[\"mpg\"].quantile(0.25)"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:43.893561Z",
          "iopub.execute_input": "2024-09-03T12:01:43.893935Z",
          "iopub.status.idle": "2024-09-03T12:01:43.909572Z",
          "shell.execute_reply.started": "2024-09-03T12:01:43.893878Z",
          "shell.execute_reply": "2024-09-03T12:01:43.908333Z"
        },
        "trusted": true,
        "id": "T52-C8Fv3nZL",
        "outputId": "99a97a48-802d-4a1e-fd09-f41fbae561f8"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 13,
          "output_type": "execute_result",
          "data": {
            "text/plain": "7.375"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The boxplots we learned to create in the lesson on plotting are just visual representations of the five number summary and IQR:"
      ],
      "metadata": {
        "id": "zbtDz7oL3nZL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars.boxplot(column=\"mpg\",\n",
        "               return_type='axes',\n",
        "               figsize=(8,8))\n",
        "\n",
        "plt.text(x=0.74, y=22.25, s=\"3rd Quartile\")\n",
        "plt.text(x=0.8, y=18.75, s=\"Median\")\n",
        "plt.text(x=0.75, y=15.5, s=\"1st Quartile\")\n",
        "plt.text(x=0.9, y=10, s=\"Min\")\n",
        "plt.text(x=0.9, y=33.5, s=\"Max\")\n",
        "plt.text(x=0.7, y=19.5, s=\"IQR\", rotation=90, size=25);"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:43.911376Z",
          "iopub.execute_input": "2024-09-03T12:01:43.911881Z",
          "iopub.status.idle": "2024-09-03T12:01:44.133664Z",
          "shell.execute_reply.started": "2024-09-03T12:01:43.911795Z",
          "shell.execute_reply": "2024-09-03T12:01:44.132636Z"
        },
        "trusted": true,
        "id": "286CT9_X3nZL",
        "outputId": "ffa7e068-3bd4-439b-c9da-8f749024e1c3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 576x576 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Variance and standard deviation are two other common measures of spread. The variance of a distribution is the average of the squared deviations (differences) from the mean. Use df.var() to check variance:"
      ],
      "metadata": {
        "id": "Oe_X5hby3nZL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars[\"mpg\"].var()"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:28:21.883842Z",
          "iopub.execute_input": "2024-09-03T12:28:21.884241Z",
          "iopub.status.idle": "2024-09-03T12:28:21.891339Z",
          "shell.execute_reply.started": "2024-09-03T12:28:21.884161Z",
          "shell.execute_reply": "2024-09-03T12:28:21.890245Z"
        },
        "trusted": true,
        "id": "QfJrK5Wb3nZL",
        "outputId": "810eb83b-5cea-4a6b-c4ff-7faed47c8888"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 33,
          "output_type": "execute_result",
          "data": {
            "text/plain": "36.32410282258065"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "The standard deviation is the square root of the variance. Standard deviation can be more interpretable than variance, since the standard deviation is expressed in terms of the same units as the variable in question while variance is expressed in terms of units squared. Use df.std() to check the standard deviation:"
      ],
      "metadata": {
        "id": "dq89js2J3nZM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars[\"mpg\"].std()"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:28:29.724105Z",
          "iopub.execute_input": "2024-09-03T12:28:29.724517Z",
          "iopub.status.idle": "2024-09-03T12:28:29.732030Z",
          "shell.execute_reply.started": "2024-09-03T12:28:29.724456Z",
          "shell.execute_reply": "2024-09-03T12:28:29.730750Z"
        },
        "trusted": true,
        "id": "P0pBr8a73nZM",
        "outputId": "065df48c-fe74-4e28-de54-b408047dad85"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 34,
          "output_type": "execute_result",
          "data": {
            "text/plain": "6.026948052089105"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since variance and standard deviation are both derived from the mean, they are susceptible to the influence of data skew and outliers. **Median absolute deviation (MAD)** is an alternative measure of spread based on the median, which inherits the median's robustness against the influence of skew and outliers. It is the median of the absolute value of the deviations from the median:"
      ],
      "metadata": {
        "id": "bFXXXtDk3nZM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "abs_median_devs = abs(mtcars[\"mpg\"] - mtcars[\"mpg\"].median())\n",
        "\n",
        "abs_median_devs.median() * 1.4826"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:44.160742Z",
          "iopub.execute_input": "2024-09-03T12:01:44.161249Z",
          "iopub.status.idle": "2024-09-03T12:01:44.195698Z",
          "shell.execute_reply.started": "2024-09-03T12:01:44.161172Z",
          "shell.execute_reply": "2024-09-03T12:01:44.194096Z"
        },
        "trusted": true,
        "id": "aaJTUDJP3nZM",
        "outputId": "86e7cf6b-160b-48ae-e8dc-a5e6cd61b98d"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 17,
          "output_type": "execute_result",
          "data": {
            "text/plain": "5.411490000000001"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "*Note: The MAD is often multiplied by a scaling factor of 1.4826.*"
      ],
      "metadata": {
        "id": "lTma03Dw3nZM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Skewness and Kurtosis"
      ],
      "metadata": {
        "id": "Odk7BGlL3nZM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Beyond measures of center and spread, descriptive statistics include measures that give you a sense of the shape of a distribution. Skewness measures the skew or asymmetry of a distribution while kurtosis measures how much data is in the tails of a distribution v.s. the center. We won't go into the exact calculations behind skewness and kurtosis, but they are essentially just statistics that take the idea of variance a step further: while variance involves squaring deviations from the mean, skewness involves cubing deviations from the mean and kurtosis involves raising deviations from the mean to the 4th power.\n",
        "\n",
        "Pandas has built in functions for checking skewness and kurtosis, df.skew() and df.kurt() respectively:"
      ],
      "metadata": {
        "id": "aNoMku693nZS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars[\"mpg\"].skew()  # Check skewness"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:44.197429Z",
          "iopub.execute_input": "2024-09-03T12:01:44.197778Z",
          "iopub.status.idle": "2024-09-03T12:01:44.205275Z",
          "shell.execute_reply.started": "2024-09-03T12:01:44.197715Z",
          "shell.execute_reply": "2024-09-03T12:01:44.204323Z"
        },
        "trusted": true,
        "id": "0aTjOer43nZS",
        "outputId": "625c71b0-78c4-4f77-c482-4f7389b3a826"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 18,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.6723771376290805"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mtcars[\"mpg\"].kurt()  # Check kurtosis"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:44.206853Z",
          "iopub.execute_input": "2024-09-03T12:01:44.207161Z",
          "iopub.status.idle": "2024-09-03T12:01:44.218941Z",
          "shell.execute_reply.started": "2024-09-03T12:01:44.207112Z",
          "shell.execute_reply": "2024-09-03T12:01:44.217789Z"
        },
        "trusted": true,
        "id": "_UV9cfdl3nZS",
        "outputId": "21d9eaba-38da-47ee-dcad-17954f8ae084"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 19,
          "output_type": "execute_result",
          "data": {
            "text/plain": "-0.0220062914240855"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "To explore these two measures further, let's create some dummy data and inspect it:"
      ],
      "metadata": {
        "id": "XO7-aVzl3nZS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "norm_data = np.random.normal(size=100000)\n",
        "skewed_data = np.concatenate((np.random.normal(size=35000)+2,\n",
        "                             np.random.exponential(size=65000)),\n",
        "                             axis=0)\n",
        "uniform_data = np.random.uniform(0,2, size=100000)\n",
        "peaked_data = np.concatenate((np.random.exponential(size=50000),\n",
        "                             np.random.exponential(size=50000)*(-1)),\n",
        "                             axis=0)\n",
        "\n",
        "data_df = pd.DataFrame({\"norm\":norm_data,\n",
        "                       \"skewed\":skewed_data,\n",
        "                       \"uniform\":uniform_data,\n",
        "                       \"peaked\":peaked_data})"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:44.220973Z",
          "iopub.execute_input": "2024-09-03T12:01:44.221309Z",
          "iopub.status.idle": "2024-09-03T12:01:44.258378Z",
          "shell.execute_reply.started": "2024-09-03T12:01:44.221241Z",
          "shell.execute_reply": "2024-09-03T12:01:44.257561Z"
        },
        "trusted": true,
        "id": "Ag6ju6cI3nZS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data_df.plot(kind=\"density\",\n",
        "            figsize=(10,10),\n",
        "            xlim=(-5,5));"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:01:44.260059Z",
          "iopub.execute_input": "2024-09-03T12:01:44.260492Z",
          "iopub.status.idle": "2024-09-03T12:02:39.479633Z",
          "shell.execute_reply.started": "2024-09-03T12:01:44.260416Z",
          "shell.execute_reply": "2024-09-03T12:02:39.478439Z"
        },
        "trusted": true,
        "id": "38VFPJsl3nZT",
        "outputId": "5c6f2499-d063-4c5a-9a89-564697a5e9df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 720x720 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now let's check the skewness of each of the distributions. Since skewness measures asymmetry, we'd expect to see low skewness for all of the distributions except the skewed one, because all the others are roughly symmetric:"
      ],
      "metadata": {
        "id": "b4sUeHcn3nZT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data_df.skew()"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:02:39.481543Z",
          "iopub.execute_input": "2024-09-03T12:02:39.481921Z",
          "iopub.status.idle": "2024-09-03T12:02:39.515631Z",
          "shell.execute_reply.started": "2024-09-03T12:02:39.481852Z",
          "shell.execute_reply": "2024-09-03T12:02:39.514647Z"
        },
        "trusted": true,
        "id": "1Thcv6md3nZT",
        "outputId": "518a0462-8aed-4398-bb8d-3ad03384effc"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 22,
          "output_type": "execute_result",
          "data": {
            "text/plain": "norm      -0.004220\nskewed     0.981826\nuniform    0.001333\npeaked    -0.002365\ndtype: float64"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now let's check kurtosis."
      ],
      "metadata": {
        "id": "lCbXR68O3nZT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data_df.kurt()"
      ],
      "metadata": {
        "execution": {
          "iopub.status.busy": "2024-09-03T12:02:39.517156Z",
          "iopub.execute_input": "2024-09-03T12:02:39.517532Z",
          "iopub.status.idle": "2024-09-03T12:02:39.547894Z",
          "shell.execute_reply.started": "2024-09-03T12:02:39.517462Z",
          "shell.execute_reply": "2024-09-03T12:02:39.546638Z"
        },
        "trusted": true,
        "id": "ZSjMfa9e3nZT",
        "outputId": "e0eef3c2-9b4c-4ff2-e382-76ddf2ca3ee3"
      },
      "execution_count": null,
      "outputs": [
        {
          "execution_count": 23,
          "output_type": "execute_result",
          "data": {
            "text/plain": "norm      -0.025551\nskewed     1.215893\nuniform   -1.202284\npeaked     3.191907\ndtype: float64"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see from the output, the normally distributed data has a kurtosis near zero, the flat distribution has negative kurtosis and the two distributions with more data in the tails vs the center have higher kurtosis."
      ],
      "metadata": {
        "id": "MQ7d2mMa3nZU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Wrap Up"
      ],
      "metadata": {
        "id": "32z0pFCV3nZU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Descriptive statistics help you explore features of your data, like center, spread and shape by summarizing them with numerical measurements. Descriptive statistics help inform the direction of an analysis and let you communicate your insights to others quickly and succinctly. In addition, certain values, like the mean and variance, are used in all sorts of statistical tests and predictive models.\n",
        "\n",
        "In this lesson, we generated a lot of random data to illustrate concepts, but we haven't actually learned much about the functions we've been using to generate random data. In the next lesson, we'll learn about probability distributions, including how to draw random data from them."
      ],
      "metadata": {
        "id": "KnJhPl7d3nZU"
      }
    }
  ]
}