03-dispersion.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dispersion "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib \n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "sns.set(color_codes=True)\n",
    "sns.set_style(\"white\")     # See more styling options here: https://seaborn.pydata.org/tutorial/aesthetics.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11500179857925275"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform(low=0.0, high=1.0)      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.22936818, 0.87022333, 0.11079194, 0.30944805, 0.81470302,\n",
       "       0.98277116, 0.54072136, 0.59734297, 0.03738012, 0.562742  ])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform(low=0.0, high=1.0, size = 10)\n",
    "# All values equally likely. Sort of like     [  0.0   0.2   0.4    0.6    0.8   1.0 ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating a LOT of numbers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_samples = 10000   # get rid of 'magic numbers'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "uniform_vals = np.random.uniform(low=0.0, high=10.0, size = num_samples)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(uniform_vals, bins=20, kde=False)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Value');\n",
    "plt.title(\"Unform Values\")\n",
    "sns.despine(offset=10, trim=True);  # move axes away \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal_vals = np.random.normal(loc=5.0, scale=10.0, size = num_samples)     \n",
    "# More values closer to `loc`    ... Sorf of like [ 1 5 5 5 5 7 ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(normal_vals, bins=20, kde=False)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Value');\n",
    "plt.title(\"Normal Values\")\n",
    "sns.despine(offset=10, trim=True);  # move axes away \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform vals mean: 4.986530741552067\n",
      "Normal vals mean:  5.021687174353235\n"
     ]
    }
   ],
   "source": [
    "print(\"Uniform vals mean:\", np.mean(uniform_vals))\n",
    "print(\"Normal vals mean: \", np.mean(normal_vals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform vals variance: 8.298200318710768\n",
      "Normal vals variance:  101.43493559335936\n"
     ]
    }
   ],
   "source": [
    "print(\"Uniform vals variance:\", np.var(uniform_vals))\n",
    "print(\"Normal vals variance: \", np.var(normal_vals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform vals sd: 2.8806597019972298\n",
      "Normal vals sd:  10.071491229870547\n"
     ]
    }
   ],
   "source": [
    "print(\"Uniform vals sd:\", np.std(uniform_vals))\n",
    "print(\"Normal vals sd: \", np.std(normal_vals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal_vals = np.random.normal(loc=5.0, scale=10.0, size = num_samples)\n",
    "\n",
    "nv_mean = np.mean(normal_vals)\n",
    "nv_sd = np.std(normal_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(normal_vals, bins=20, kde=False)\n",
    "plt.xlim(-60, 60)\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Value');\n",
    "plt.title(\"Normal Values\")\n",
    "sns.despine(offset=10, trim=True);  # move axes away \n",
    "\n",
    "# plot the SD line \n",
    "x_c, y_c = ([nv_mean, nv_mean], [0, 1500])\n",
    "plt.plot(x_c, y_c, color='green', linewidth=2)\n",
    "\n",
    "x_c, y_c = ([nv_mean + nv_sd, nv_mean + nv_sd], [0, 1500])\n",
    "plt.plot(x_c, y_c, color='red', linewidth=2)\n",
    "\n",
    "\n",
    "x_c, y_c = ([nv_mean - nv_sd, nv_mean - nv_sd], [0, 1500])\n",
    "plt.plot(x_c, y_c, color='red', linewidth=2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal_vals_2 = np.random.normal(loc=5.0, scale=15.0, size = num_samples)\n",
    "nv_mean_2 = np.mean(normal_vals_2)\n",
    "nv_sd_2 = np.std(normal_vals_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(normal_vals_2, bins=20, kde=False)\n",
    "plt.xlim(-60, 60)\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Value');\n",
    "plt.title(\"Normal Values\")\n",
    "sns.despine(offset=10, trim=True);  # move axes away \n",
    "\n",
    "# plot the SD line \n",
    "x_c, y_c = ([nv_mean_2, nv_mean_2], [0, 1500])\n",
    "plt.plot(x_c, y_c, color='green', linewidth=2)\n",
    "\n",
    "x_c, y_c = ([nv_mean_2 + nv_sd_2, nv_mean_2 + nv_sd_2], [0, 1500])\n",
    "plt.plot(x_c, y_c, color='red', linewidth=2)\n",
    "\n",
    "\n",
    "x_c, y_c = ([nv_mean_2 - nv_sd_2, nv_mean_2 - nv_sd_2], [0, 1500])\n",
    "plt.plot(x_c, y_c, color='red', linewidth=2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's put both together\n",
    "normal_vals = np.random.normal(loc=5.0, scale=10.0, size = num_samples)\n",
    "normal_vals_2 = np.random.normal(loc=5.0, scale=15.0, size = num_samples)\n",
    "\n",
    "def plot_dist(vals, label): \n",
    "    nv_mean = np.mean(vals)\n",
    "    nv_sd = np.std(vals)\n",
    "    \n",
    "    sns.distplot(vals, bins=20, kde=False)\n",
    "    \n",
    "    plt.xlim(-60, 60)\n",
    "\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.xlabel('Value')\n",
    "    plt.title(label)\n",
    "    sns.despine(offset=10, trim=True);  # move axes away \n",
    "\n",
    "    # plot the SD line \n",
    "    x_c, y_c = ([nv_mean, nv_mean], [0, 1500])\n",
    "    plt.plot(x_c, y_c, color='green', linewidth=1)\n",
    "\n",
    "    x_c, y_c = ([nv_mean + nv_sd, nv_mean + nv_sd], [0, 1500])\n",
    "    plt.plot(x_c, y_c, color='red', linewidth=1)\n",
    "\n",
    "\n",
    "    x_c, y_c = ([nv_mean - nv_sd, nv_mean - nv_sd], [0, 1500])\n",
    "    plt.plot(x_c, y_c, color='red', linewidth=1)\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "    \n",
    "plot_dist(normal_vals, \"Less Variant\")\n",
    "plot_dist(normal_vals_2, \"More Variant\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Working with Real World Datasets "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install sklearn "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nam/Dropbox/Teaching/FASTu/csxxx-stats-prob/notebooks/stats-env/lib/python3.8/site-packages/sklearn/utils/deprecation.py:143: FutureWarning: The sklearn.datasets.california_housing module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets.california_housing import fetch_california_housing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "houses = fetch_california_housing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _california_housing_dataset:\n",
      "\n",
      "California Housing dataset\n",
      "--------------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 20640\n",
      "\n",
      "    :Number of Attributes: 8 numeric, predictive attributes and the target\n",
      "\n",
      "    :Attribute Information:\n",
      "        - MedInc        median income in block\n",
      "        - HouseAge      median house age in block\n",
      "        - AveRooms      average number of rooms\n",
      "        - AveBedrms     average number of bedrooms\n",
      "        - Population    block population\n",
      "        - AveOccup      average house occupancy\n",
      "        - Latitude      house block latitude\n",
      "        - Longitude     house block longitude\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "This dataset was obtained from the StatLib repository.\n",
      "http://lib.stat.cmu.edu/datasets/\n",
      "\n",
      "The target variable is the median house value for California districts.\n",
      "\n",
      "This dataset was derived from the 1990 U.S. census, using one row per census\n",
      "block group. A block group is the smallest geographical unit for which the U.S.\n",
      "Census Bureau publishes sample data (a block group typically has a population\n",
      "of 600 to 3,000 people).\n",
      "\n",
      "It can be downloaded/loaded using the\n",
      ":func:`sklearn.datasets.fetch_california_housing` function.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "    - Pace, R. Kelley and Ronald Barry, Sparse Spatial Autoregressions,\n",
      "      Statistics and Probability Letters, 33 (1997) 291-297\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(houses.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['MedInc',\n",
       " 'HouseAge',\n",
       " 'AveRooms',\n",
       " 'AveBedrms',\n",
       " 'Population',\n",
       " 'AveOccup',\n",
       " 'Latitude',\n",
       " 'Longitude']"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20640, 8)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   8.3252    ,   41.        ,    6.98412698,    1.02380952,\n",
       "        322.        ,    2.55555556,   37.88      , -122.23      ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.32520000e+00,  4.10000000e+01,  6.98412698e+00,\n",
       "         1.02380952e+00,  3.22000000e+02,  2.55555556e+00,\n",
       "         3.78800000e+01, -1.22230000e+02],\n",
       "       [ 8.30140000e+00,  2.10000000e+01,  6.23813708e+00,\n",
       "         9.71880492e-01,  2.40100000e+03,  2.10984183e+00,\n",
       "         3.78600000e+01, -1.22220000e+02],\n",
       "       [ 7.25740000e+00,  5.20000000e+01,  8.28813559e+00,\n",
       "         1.07344633e+00,  4.96000000e+02,  2.80225989e+00,\n",
       "         3.78500000e+01, -1.22240000e+02],\n",
       "       [ 5.64310000e+00,  5.20000000e+01,  5.81735160e+00,\n",
       "         1.07305936e+00,  5.58000000e+02,  2.54794521e+00,\n",
       "         3.78500000e+01, -1.22250000e+02],\n",
       "       [ 3.84620000e+00,  5.20000000e+01,  6.28185328e+00,\n",
       "         1.08108108e+00,  5.65000000e+02,  2.18146718e+00,\n",
       "         3.78500000e+01, -1.22250000e+02],\n",
       "       [ 4.03680000e+00,  5.20000000e+01,  4.76165803e+00,\n",
       "         1.10362694e+00,  4.13000000e+02,  2.13989637e+00,\n",
       "         3.78500000e+01, -1.22250000e+02],\n",
       "       [ 3.65910000e+00,  5.20000000e+01,  4.93190661e+00,\n",
       "         9.51361868e-01,  1.09400000e+03,  2.12840467e+00,\n",
       "         3.78400000e+01, -1.22250000e+02],\n",
       "       [ 3.12000000e+00,  5.20000000e+01,  4.79752705e+00,\n",
       "         1.06182380e+00,  1.15700000e+03,  1.78825348e+00,\n",
       "         3.78400000e+01, -1.22250000e+02],\n",
       "       [ 2.08040000e+00,  4.20000000e+01,  4.29411765e+00,\n",
       "         1.11764706e+00,  1.20600000e+03,  2.02689076e+00,\n",
       "         3.78400000e+01, -1.22260000e+02],\n",
       "       [ 3.69120000e+00,  5.20000000e+01,  4.97058824e+00,\n",
       "         9.90196078e-01,  1.55100000e+03,  2.17226891e+00,\n",
       "         3.78400000e+01, -1.22250000e+02]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses.data[:10]    # add   .shape to see what changed "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([   8.3252    ,   41.        ,    6.98412698,    1.02380952,\n",
       "         322.        ,    2.55555556,   37.88      , -122.23      ]),\n",
       " array([ 8.30140000e+00,  2.10000000e+01,  6.23813708e+00,  9.71880492e-01,\n",
       "         2.40100000e+03,  2.10984183e+00,  3.78600000e+01, -1.22220000e+02]),\n",
       " array([   7.2574    ,   52.        ,    8.28813559,    1.07344633,\n",
       "         496.        ,    2.80225989,   37.85      , -122.24      ]),\n",
       " array([   5.6431    ,   52.        ,    5.8173516 ,    1.07305936,\n",
       "         558.        ,    2.54794521,   37.85      , -122.25      ]),\n",
       " array([   3.8462    ,   52.        ,    6.28185328,    1.08108108,\n",
       "         565.        ,    2.18146718,   37.85      , -122.25      ]),\n",
       " array([   4.0368    ,   52.        ,    4.76165803,    1.10362694,\n",
       "         413.        ,    2.13989637,   37.85      , -122.25      ]),\n",
       " array([ 3.65910000e+00,  5.20000000e+01,  4.93190661e+00,  9.51361868e-01,\n",
       "         1.09400000e+03,  2.12840467e+00,  3.78400000e+01, -1.22250000e+02]),\n",
       " array([ 3.12000000e+00,  5.20000000e+01,  4.79752705e+00,  1.06182380e+00,\n",
       "         1.15700000e+03,  1.78825348e+00,  3.78400000e+01, -1.22250000e+02]),\n",
       " array([ 2.08040000e+00,  4.20000000e+01,  4.29411765e+00,  1.11764706e+00,\n",
       "         1.20600000e+03,  2.02689076e+00,  3.78400000e+01, -1.22260000e+02]),\n",
       " array([ 3.69120000e+00,  5.20000000e+01,  4.97058824e+00,  9.90196078e-01,\n",
       "         1.55100000e+03,  2.17226891e+00,  3.78400000e+01, -1.22250000e+02])]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[ x for x in  houses.data[:10]  ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "med_incs = [   x[0] for x in  houses.data     ]   # list comprehension "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[8.3252, 8.3014, 7.2574, 5.6431, 3.8462, 4.0368, 3.6591, 3.12, 2.0804, 3.6912]\n"
     ]
    }
   ],
   "source": [
    "print(med_incs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8706710029069766"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(med_incs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.609147689697444"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(med_incs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3hIeHIzs7G97e3liwYAGWLVsGT09PxMTEIDk5GdOmTTNX2fedu71tvnvPhyWuhIjoP8x2WGzIkCH4+OOPIZfLcfHiRej1etjb26OsrAwxMTFQqVRITEyEwWBAfn4+evbsiR49ekAul0OlUkGtVqO0tBSNjY3w9PQEAAQFBUGtVpurZCIikohZx1xsbGyQmJiIgIAAeHl5QafTYdiwYVixYgWSk5Px/fffIyUlBZWVlXBxcTH2UygUqKioaNXu4uKCiooKc5ZMREQSMPuA/rx585Cbm4vy8nLk5uZiw4YNUCgUcHBwQGhoKLKzs2EwGCCTyYx9hBCQyWQ3bScioo7NbGMuZ86cQVNTE37/+9/DwcEBvr6+yMjIgJOTE/z8/ABcCwu5XA5XV1doNBpjX41GA4VC0aq9qqqqxVgNWYZObzD5RIK25nOwl/MxyUQPOLOFS0lJCRITE7F9+3YAQFZWFp555hmsWLECw4YNQ6dOnbBjxw5MnDgRHh4eOHv2LIqLi9G9e3ekp6dj0qRJcHNzg52dHfLy8jBo0CCkpqZCqVSaq2QykbZZj/x/VZk0b1snHDztrmC4ED3gzBYu3t7eyM/Px4QJE2BtbQ1fX1/MnTsXDz/8MKZOnQqdTgdfX18EBgYCAFatWoWIiAhotVp4e3vD398fAJCQkIDY2FjU1dWhX79+CAsLM1fJREQkEZkQQli6CHMoKSnB6NGjkZWVhe7du1u6HOn9e+xJnXP2rrq793wYp4ovma3vmC96AQD2+bau72l3BRTOne7qsyVzfezuwfznT2RxvEKfiIgkx3AhIiLJMVyIiEhyDBciIpIcw4WIiCTHcCEiIskxXIiISHIMFyIikhzDhYiIJMdwISIiyTFciIhIcgwXIiKSHMOFiIgkx3AhIiLJMVyIiEhyDBciIpIcw4WIiCRn1nBZv349xo4di4CAAGzZsgUAkJOTA5VKBV9fX6xbt844b2FhIYKCguDn54eFCxdCp9MBAMrKyhASEgJ/f3+88sorqK+vN2fJREQkAbOFy5EjR3D48GGkpaVh586dSEpKwsmTJxETE4ONGzciIyMDBQUFyM7OBgAsWLAAcXFx2L9/P4QQSE5OBgAsXrwY06ZNg1qtRv/+/bFx40ZzlUxERBIxW7gMGTIEH3/8MeRyOS5evAi9Xo8rV66gZ8+e6NGjB+RyOVQqFdRqNUpLS9HY2AhPT08AQFBQENRqNZqbm3H06FH4+fm1aCcioo7NrIfFbGxskJiYiICAAHh5eaGyshIuLi7G9xUKBSoqKlq1u7i4oKKiApcuXYKjoyPkcnmLdiIi6tjMPqA/b9485Obmory8HEVFRZDJZMb3hBCQyWQwGAxttl//+9dunCYioo7HbOFy5swZFBYWAgAcHBzg6+uL7777DhqNxjiPRqOBQqGAq6tri/aqqiooFAo4OzujtrYWer2+xfxERNSxmS1cSkpKEBsbi6amJjQ1NSErKwvBwcE4e/YsiouLodfrkZ6eDqVSCTc3N9jZ2SEvLw8AkJqaCqVSCRsbGwwePBgZGRkAgD179kCpVJqrZCIikojcXAv29vZGfn4+JkyYAGtra/j6+iIgIADOzs6IiIiAVquFt7c3/P39AQAJCQmIjY1FXV0d+vXrh7CwMABAfHw8oqOjsWnTJnTr1g1r1641V8lERCQRmRBCWLoIcygpKcHo0aORlZWF7t27W7oc6f177Emdc/auurv3fBinii+Zre+YL3oBAPb5tq7vaXcFFM6d7uqzJXN97O7B/OdPZHG8Qp+IiCTHcCEiIskxXIiISHIMFyIikhzDhYiIJMdwISIiyTFciIhIcgwXIiKSHMOFiIgkx3AhIiLJMVyIiEhyDBciIpIcw4WIiCTHcCEiIskxXIiISHImPSwsKSkJEydOhKOjo7nrod8And6Ayuqrd9XXwV6OLp1sJa6IiKRmUricOnUKfn5+ePbZZxEcHIw//OEP5q6LHmDaZj3y/1V1V32fdlcwXIjuAyaFy7Jly1BXV4e9e/di8eLFEEJg6tSpUKlUsLOzu2m/9957D/v27QNw7bHHUVFReOutt5CXlwcHBwcAwNy5c+Hj44OcnBysXLkSWq0WY8aMQWRkJACgsLAQCxcuRH19PQYPHozFixdDLjfb05mJiEgCJo+5ODo6wt/fH4GBgbh8+TI++eQT+Pv748CBA23On5OTg2+//Ra7d+/Gnj178NNPPyEzMxMFBQXYunUrUlNTkZqaCh8fHzQ2NiImJgYbN25ERkYGCgoKkJ2dDQBYsGAB4uLisH//fgghkJycLM2aExGR2ZgULrm5uXj99dfh7++PX375BRs2bMCuXbvw0UcfIS4urs0+Li4uiI6Ohq2tLWxsbNC7d2+UlZWhrKwMMTExUKlUSExMhMFgQH5+Pnr27IkePXpALpdDpVJBrVajtLQUjY2N8PT0BAAEBQVBrVZLt/ZERGQWJh1fWrx4MaZNm4alS5eiS5cuxvbHHnsMU6ZMabPPk08+aXxdVFSEffv2Ydu2bThy5Aji4+PRpUsXhIeHIyUlBZ06dYKLi4txfoVCgYqKClRWVrZod3FxQUVFxR2vJBERtS+T9lzS0tLg5OSELl26QKPR4MMPP4TBYAAAzJs375Z9T58+jVmzZiEqKgqPP/44NmzYAIVCAQcHB4SGhiI7OxsGgwEymczYRwgBmUx203YiIurYTAqXpUuX4uDBg9c6WFkhLy8PK1asuG2/vLw8zJw5E2+88QYmTpyIU6dOYf/+/cb3hRCQy+VwdXWFRqMxtms0GigUilbtVVVVUCgUpq4bERFZiEnh8sMPP2Dt2rUAgEceeQTr16/Hd999d8s+5eXleO2115CQkICAgAAA18JkxYoVqKmpQXNzM3bs2AEfHx94eHjg7NmzKC4uhl6vR3p6OpRKJdzc3GBnZ4e8vDwAQGpqKpRK5b2sLxERtQOTxlyam5vR1NQEW9tr1xfodLrb9tm8eTO0Wi1WrVplbAsODsacOXMwdepU6HQ6+Pr6IjAwEACwatUqREREQKvVwtvbG/7+/gCAhIQExMbGoq6uDv369UNYWNgdryQREbUvk8Ll2WefxezZszF+/HjIZDKkp6fD29v7ln1iY2MRGxvb5nshISGt2ry8vJCWltaqvW/fvkhJSTGlTCIi6iBMCpeoqChs27YNWVlZkMvl8PHxQXBwsLlrIyKi+5RJ4WJtbY2wsDAekiIiIpOYFC5ffvmlcSBeCGFsP3bsmNkKIyKi+5dJ4fLOO+8gOjoaTz31FK8zISKi2zIpXH73u9/B19fX3LUQEdEDwqTrXDw8PIw3kiQiIrodk/ZcsrOzsXXrVtjY2MDGxsZ4GxaOuRARUVtMCpcPP/zQzGUQEdGDxKTDYm5ubvjxxx+RnJwMZ2dn/PDDD3BzczN3bUREdJ8yKVz+7//+D9u3b4darUZjYyPee+89bNiwwdy1ERHRfcqkcPn888/x97//HQ4ODnj44YeRnJyM9PR0c9dGRET3KZPCRS6XG29aCVw7NZnPsSciopsxKSG6deuGgwcPQiaToampCZs3b+aYCxER3ZRJ4bJo0SJERUXh1KlT8PT0hIeHBxISEsxdGxER3adMCpeuXbvio48+QkNDA/R6PRwdHc1dFxER3cdMCpctW7a02f7iiy9KWgwRET0YTAqXn3/+2fi6qakJR48ehZeXl9mKIiKi+5tJ4bJy5coW0xUVFVi4cOFt+7333nvYt28fAMDb2xtRUVHIycnBypUrodVqMWbMGERGRgIACgsLsXDhQtTX12Pw4MFYvHgx5HI5ysrKsGDBAly8eBG9evVCQkICOnfufKfrSURE7cikU5Fv1LVrV5SWlt5ynpycHHz77bfYvXs39uzZg59++gnp6emIiYnBxo0bkZGRgYKCAuMNMRcsWIC4uDjs378fQggkJycDABYvXoxp06ZBrVajf//+2Lhx492UTERE7eiOx1yEECgoKMAjjzxyyz4uLi6Ijo42Xh/Tu3dvFBUVoWfPnujRowcAQKVSQa1W44knnkBjYyM8PT0BAEFBQUhMTMTzzz+Po0ePGu8GEBQUhOnTp2PBggV3vqZERNRu7njMBbh23UtUVNQt+zz55JPG10VFRdi3bx+mT58OFxcXY7tCoUBFRQUqKytbtLu4uKCiogKXLl2Co6Oj8YLN6+1ERNSx3dWYy504ffo0wsPDERUVBWtraxQVFRnfu37rfoPB0OIJl9fbr//9a3wSJhFRx2dSuISGht7yl/rHH3/cZnteXh7mzZuHmJgYBAQE4MiRI9BoNMb3NRoNFAoFXF1dW7RXVVVBoVDA2dkZtbW10Ov1sLa2Ns5PREQdm0kD+v3794e9vT3CwsIwe/ZsPProo3ByckJISAhCQkLa7FNeXo7XXnsNCQkJCAgIAHDtiZZnz55FcXEx9Ho90tPToVQq4ebmBjs7O+Tl5QEAUlNToVQqYWNjg8GDByMjIwMAsGfPHiiVSinWm4iIzMikPZdjx47hk08+gbW1NQBg5MiRmDJlCvz8/G7aZ/PmzdBqtVi1apWxLTg4GKtWrUJERAS0Wi28vb3h7+8PAEhISEBsbCzq6urQr18/hIWFAQDi4+MRHR2NTZs2oVu3bli7du1drywREbUPk8KluroaWq0WnTp1AgDU19ejsbHxln1iY2MRGxvb5ntpaWmt2vr27YuUlJRW7W5ubkhKSjKlTCIi6iBMCpfAwEC88MIL8PHxgRAC+/btM+5ZEBER3cikcJk/fz6eeuopHD58GHZ2dliyZAmGDBli7tp+E2qvNqGhUXfH/XhaAxF1ZCY/8atr16548sknERQUhJ9++smcNf2mNDTqcOxU5R338zdDLUREUjEpXHbu3IkPPvgAWq0WPj4+ePXVVxEZGYkpU6aYuz6iFnR6Ayqrr95VXwd7Obp0sr39jER0z0wKl61bt2LHjh2YPn06HnnkEezatQsvvfQSw4XanbZZj/x/Vd1V36fdFQwXonZi0nUuVlZWLR4Q1q1bN+NpyURERDcyKVycnJxQWFhovEo/LS0NDz30kFkLIyKi+5dJh8ViYmIwf/58nDt3DiNGjICdnR1vfU9ERDdlUrg0NjYiNTUVRUVF0Ov16NWrF2xsbMxdGxER3adMOiz2P//zP7C2tkbv3r3Rp08fBgsREd2SSeHi7u6OvXv3oqysDJcvXzb+ISIiaotJh8WysrKgVqtbtMlkMhQWFpqlKCIiur+ZFC4//vijuesgIqIHyC0Piy1atMj4urq62uzFEBHRg+GW4VJQUGB8PXv2bLMXQ0RED4ZbhosQos3XREREt2LS2WIAjFfnExER3c4tw8VgMKCmpgaXL1+GXq83vr6TU5Hr6uoQGBiIkpISAMBbb70FX19fjB8/HuPHj0dmZiYAICcnByqVCr6+vli3bp2xf2FhIYKCguDn54eFCxdCp7vzZ58QEVH7uuXZYj///DOGDRtmPCQ2dOhQ43umnIp84sQJxMbGoqioyNhWUFCArVu3QqH4z+OuGhsbERMTg6SkJHTr1g3h4eHIzs6Gt7c3FixYgGXLlsHT0xMxMTFITk7GtGnT7mZdiYiondwyXE6ePHlPC09OTkZ8fDyioqIAAA0NDSgrK0NMTAwqKirg4+ODuXPnIj8/Hz179kSPHj0AACqVCmq1Gk888QQaGxvh6ekJAAgKCkJiYiLDhYiogzP5SZR3Y/ny5S2mq6qqMGzYMMTHx6NLly4IDw9HSkoKOnXqBBcXF+N8CoUCFRUVqKysbNHu4uKCiooKc5ZMREQSMHlAXwo9evTAhg0boFAo4ODggNDQUGRnZ8NgMLQ4YUAIAZlMdtN2IiLq2No1XE6dOoX9+/cbp4UQkMvlcHV1hUajMbZrNBooFIpW7VVVVS3GaoiIqGNq13ARQmDFihWoqalBc3MzduzYAR8fH3h4eODs2bMoLi6GXq9Heno6lEol3NzcYGdnh7y8PABAamoqlEple5ZMRER3waxjLjfq27cv5syZg6lTp0Kn08HX1xeBgYEAgFWrViEiIgJarRbe3t7w9/cHACQkJCA2NhZ1dXXo168fwsLC2rNkIiK6C+0SLgcOHDC+DgkJQUhISKt5vLy8kP4VloEAABJcSURBVJaW1qq9b9++SElJMWt9REQkrXY9LEZERL8NDBciIpIcw4WIiCTHcCEiIskxXIiISHIMFyIikhzDhYiIJMdwISIiyTFciIhIcgwXIiKSHMOFiIgkx3AhIiLJtetdkYksSac3oLL6KgDg+lOBrk/fjoO9HF062ZqpMqIHD8OFfjO0zXrk/6sKAOD/77ZjpypN6vu0u4LhQnQHeFiMiIgkx3AhIiLJMVyIiEhyZg+Xuro6BAYGoqSkBACQk5MDlUoFX19frFu3zjhfYWEhgoKC4Ofnh4ULF0Kn0wEAysrKEBISAn9/f7zyyiuor683d8lERHSPzBouJ06cwNSpU1FUVAQAaGxsRExMDDZu3IiMjAwUFBQgOzsbALBgwQLExcVh//79EEIgOTkZALB48WJMmzYNarUa/fv3x8aNG81ZMhERScCs4ZKcnIz4+HgoFNdO/MzPz0fPnj3Ro0cPyOVyqFQqqNVqlJaWorGxEZ6engCAoKAgqNVqNDc34+jRo/Dz82vRTkREHZtZT0Vevnx5i+nKykq4uLgYpxUKBSoqKlq1u7i4oKKiApcuXYKjoyPkcnmLdiIi6tjadUDfYDBAJpMZp4UQkMlkN22//vev3ThNREQdT7uGi6urKzQajXFao9FAoVC0aq+qqoJCoYCzszNqa2uh1+tbzE9ERB1bu4aLh4cHzp49i+LiYuj1eqSnp0OpVMLNzQ12dnbIy8sDAKSmpkKpVMLGxgaDBw9GRkYGAGDPnj1QKpXtWTIREd2Fdr39i52dHVatWoWIiAhotVp4e3vD3//ajTgSEhIQGxuLuro69OvXD2FhYQCA+Ph4REdHY9OmTejWrRvWrl3bniUTEdFdaJdwOXDggPG1l5cX0tLSWs3Tt29fpKSktGp3c3NDUlKSWesjIiJp8Qp9IiKSHMOFiIgkx3AhIiLJMVyIiEhyDBciIpIcw4WIiCTHcCEiIskxXIiISHIMFyIikhzDhYiIJMdwISIiybXrjSuJ7lc6vQGV1Vfvur+DvRxdOtlKWBFRx8ZwITKBtlmP/H9V3XX/p90VDBf6TeFhMSIikhzDhYiIJMdwISIiyTFciIhIchYZ0A8NDUV1dTXk8msfv2TJEpw7dw6bNm2CTqfDjBkzEBISAgDIycnBypUrodVqMWbMGERGRlqiZCIiugPtHi5CCBQVFeGrr74yhktFRQUiIyOxa9cu2NraIjg4GEOHDkX37t0RExODpKQkdOvWDeHh4cjOzoa3t3d7l01ERHeg3cPll19+AQDMmjULly9fxpQpU9C5c2cMGzYMTk5OAAA/Pz+o1WoMGTIEPXv2RI8ePQAAKpUKarWa4UJE1MG1+5jLlStX4OXlhQ0bNuDDDz/Ep59+irKyMri4uBjnUSgUqKioQGVlZZvtRETUsbV7uAwcOBBr1qxBly5d4OzsjMmTJyMxMREymcw4jxACMpkMBoOhzXYiIurY2j1cvv/+e+Tm5hqnhRBwc3ODRqMxtmk0GigUCri6urbZTkREHVu7h0ttbS3WrFkDrVaLuro67N69G++88w5yc3NRXV2NhoYGfPHFF1AqlfDw8MDZs2dRXFwMvV6P9PR0KJXK9i6ZiIjuULsP6I8aNQonTpzAhAkTYDAYMG3aNAwaNAiRkZEICwtDc3MzJk+ejAEDBgAAVq1ahYiICGi1Wnh7e8Pf37+9SyYiojtkketcXn/9dbz++ust2lQqFVQqVat5vby8kJaW1l6lERGRBHiFPhERSY633JdA7dUmNDTq7qqvtlkvcTXUEd3L82D4LBi6HzFcJNDQqMOxU5V31de958MSV0Md0b08D4bPgqH7EQ+LERGR5BguREQkOR4WI+rgOF5D9yOGC1EHx/Eauh/xsBgREUmO4UJERJJjuBARkeQYLkREJDmGCxERSY7hQkREkuOpyEQPMF4jQ5bCcCF6gPEaGbIUhgsRSe5e7hQOcK/pQcBwISLJ3cudwgHuNT0I7otw2bt3LzZt2gSdTocZM2YgJCTE0iURPfDuZbzmXp9TxLGiO3Mve4rm2l4dPlwqKiqwbt067Nq1C7a2tggODsbQoUPxxBNPWLo0ogfavYzX3OtzijhWdGfuZU/RXNurw4dLTk4Ohg0bBicnJwCAn58f1Go15s6da+HKiKgjupe9HisrwGC4u8+9l74P4t5Whw+XyspKuLi4GKcVCgXy8/MtWFFrCudO8Pf677vu3+u/HrrzTkIAAPzv+lPv8nNN7Cu8hMU+26S+d7H97uVz77X/b62vFP1/S+71d5A5dPiLKA0GA2QymXFaCNFi+mZcXV2RlZUFV1dXc5ZHRERt6PDh4urqCo1GY5zWaDRQKBS37SeXy9G9e3fI5R1+54yI6IHT4cPlj3/8I3Jzc1FdXY2GhgZ88cUXUCqVli6LiIhuocP/t75r166IjIxEWFgYmpubMXnyZAwYMMDSZRER0S3IhBC3HnklIiK6Qx3+sBgREd1/GC5ERCQ5hgsREUmuww/oW4JOp8OFCxcsXQYRUSuurq73xSUWHb9CC7hw4QJGjx5t6TKIiFrJyspC9+7dLV3GbfFssTZwz4WIOqr7Zc+F4UJERJLjgD4REUmO4UJERJJjuBARkeQYLkREJDmGCxERSY7hQkREkmO4EBGR5BguN9i7dy/Gjh0LX19fbNu2zdLl3NR7772HgIAABAQEYM2aNZYu57ZWr16N6OhoS5dxUwcOHEBQUBDGjBmDZcuWWbqcm0pNTTV+76tXr7Z0Oa3U1dUhMDAQJSUlAICcnByoVCr4+vpi3bp1Fq7uP26sc8eOHQgMDIRKpcJbb72FpqYmC1d4zY11Xrd161aEhoZaqCoTCTK6cOGCGDVqlLh06ZKor68XKpVKnD592tJltXLo0CHxwgsvCK1WK5qamkRYWJj44osvLF3WTeXk5IihQ4eKN99809KltOncuXNixIgRory8XDQ1NYmpU6eKgwcPWrqsVq5evSqeeeYZcfHiRdHc3CwmT54sDh06ZOmyjI4fPy4CAwNFv379xPnz50VDQ4Pw9vYW586dE83NzWLWrFkdYrveWOcvv/wifHx8RG1trTAYDCIqKkps2bLF0mW2qvO606dPi5EjR4rp06dbsLrb457Lr+Tk5GDYsGFwcnJCp06d4OfnB7VabemyWnFxcUF0dDRsbW1hY2OD3r17o6yszNJlteny5ctYt24dXn75ZUuXclOZmZkYO3YsXF1dYWNjg3Xr1sHDw8PSZbWi1+thMBjQ0NAAnU4HnU4HOzs7S5dllJycjPj4eCgUCgBAfn4+evbsiR49ekAul0OlUnWIn6cb67S1tUV8fDwcHR0hk8nQp0+fDvHzdGOdANDU1IS4uDjMmzfPgpWZpuPfoKYdVVZWwsXFxTitUCiQn59vwYra9uSTTxpfFxUVYd++fdi+fbsFK7q5uLg4REZGory83NKl3FRxcTFsbGzw8ssvo7y8HM8++yxef/11S5fViqOjI+bPn48xY8bAwcEBzzzzDJ5++mlLl2W0fPnyFtNt/TxVVFS0d1mt3Finm5sb3NzcAADV1dXYtm0bVq5caYnSWrixTgD461//ikmTJt0XN67knsuvGAwGyGQy47QQosV0R3P69GnMmjULUVFR+O///m9Ll9PKZ599hm7dusHLy8vSpdySXq9Hbm4uVqxYgR07diA/Px+7d++2dFmtnDx5Ejt37sRXX32Fb775BlZWVti8ebOly7qp++3nqaKiAjNmzMCkSZMwdOhQS5fTyqFDh1BeXo5JkyZZuhSTMFx+xdXVFRqNxjit0Wha7JJ2JHl5eZg5cybeeOMNTJw40dLltCkjIwOHDh3C+PHjkZiYiAMHDmDFihWWLquVRx99FF5eXnB2doa9vT3+9Kc/dcg91m+//RZeXl545JFHYGtri6CgIBw5csTSZd3U/fTzdObMGQQHB2PixIl47bXXLF1Om9LT03H69GmMHz8esbGxKCgo6JB72EaWHvTpSK4P6F+8eFFcvXpVjBs3Tpw4ccLSZbVSVlYmhg4dKnJycixdisl27tzZYQf0jx8/Lvz8/ERNTY3Q6XQiPDxcJCcnW7qsVr755hsxbtw4UV9fLwwGg1i0aJFITEy0dFmtjBo1Spw/f140NjYKpVIpioqKhE6nE7NnzxYZGRmWLs/oep21tbXC29tb7N6929Iltel6nb92+PDhDj+gzzGXX+natSsiIyMRFhaG5uZmTJ48GQMGDLB0Wa1s3rwZWq0Wq1atMrYFBwdj6tSpFqzq/uXh4YGXXnoJ06ZNQ3NzM4YPH94hDz2MGDEC//znPxEUFAQbGxv84Q9/wJw5cyxd1k3Z2dlh1apViIiIgFarhbe3N/z9/S1dVispKSmoqqrCli1bsGXLFgDAc889h/nz51u4svsbn+dCRESS45gLERFJjuFCRESSY7gQEZHkGC5ERCQ5hgsREUmO4UK/aSUlJXB3d8f06dNbvRcdHQ13d3dUV1ff0TKXLFmC//3f/wUA/PnPf8a//vUvSWr97rvvEBgYKMmyiMyN17nQb56dnR3Onj2L0tJS4z2mrl69imPHjt3zsv/+97/f8zKI7kcMF/rNs7a2xpgxY7B3717j3Zu/+OILjB49Gh988IFxvgMHDmDTpk1obm6Gvb093nzzTQwcOBB1dXVYuHAhTp48CYVCAWtrawwaNAjAtYvx1q9fj379+mHFihU4ceIE6uvrIYTAsmXLMGjQIERHR8PR0RGnTp3ChQsX4O7ujtWrV6Nz5843rXnXrl3IzMyElZUViouLYW9vj9WrV6N3797QaDSIj4/HL7/8AisrKwQHByMsLAwXLlzA22+/jdLSUgghMGHCBLz00ksoKSnBjBkzMHz4cBQUFECv12PevHnYsWMHfvnlF/Tv3x9r166FlZUVjh07hoSEBDQ0NMDKygpz587FqFGjzPsF0f3JsjcIILKs8+fPC09PT/Hjjz8Kf39/Y/uMGTPEqVOnRJ8+fcTFixfF2bNnRWBgoKiurhZCCPHzzz+L4cOHi/r6erF8+XIRFRUlDAaDuHjxolAqlcbbsowaNUrk5+eLY8eOiYiICKHX64UQQrz//vsiPDxcCCHEm2++2eL5PBMmTBApKSmtaj18+LAICAgQQly7nc6gQYNEeXm5EEKIJUuWiKioKCGEEK+99ppYvXq1EEKIK1euiICAAFFUVCRCQkLEBx98YGxXqVQiPT1dnD9/XvTp00d8+eWXQggh4uLixKhRo0Rtba1obGwUw4cPF3l5eeLy5cvC19fXeCuSCxcuCKVSKUpLSyX8RuhBwT0XIgD9+/eHtbU1CgoK8Mgjj6C+vh59+vQxvn/o0CFUVlZi5syZxjaZTIZz584hNzcXMTExkMlkcHZ2ho+PT6vlDxw4EA899BA+/fRTnD9/Ht99912LPZORI0fC1tYWANCnTx/U1NTctuZ+/frB1dUVAPDUU08hMzMTwLXnEi1YsAAA0KVLF6SnpxsP813fE+vSpQuCgoLw9ddfw8PDAzY2NnjuuecAAI899hgGDhwIR0dHANdulV9TU4Pjx49Do9G0uLGjTCbDqVOn8F//9V+338j0m8JwIfq3cePGIS0tDc7Ozhg/fnyL9wwGA7y8vPDuu+8a28rLy413+RW/uouStbV1q2UfPHgQy5cvx4svvojRo0fj8ccfR1pamvF9e3t742uZTNZieTdzsz5yubzFre3Pnz8PJyenVss0GAzQ6XQAABsbmxZ9bGxsWn2eXq9H79698dlnnxnbKioq4OzsfNta6beHZ4sR/dv48eOhVquRkZHR6qwsLy8vHDp0CGfOnAEAZGdnY9y4cWhsbMTIkSORkpICg8GAmpoaZGVltVr2oUOHMGrUKEybNg39+/fHl19+Cb1eb5b18PLyws6dOwEAtbW1mDFjBoqLi+Hh4YFt27YZ2/fs2YM//vGPJi/X09MTxcXFOHr0KACgsLAQfn5+HeIBYNTxcM+F6N+6du2K3r17o0uXLnBycmrx3hNPPIElS5bgL3/5C4QQkMvl2LRpEzp37oyIiAjEx8djzJgxcHZ2bnE47brg4GC88cYbUKlU0Ol0GD58OL744gsYDAbJ1yMuLg5vv/02VCoVhBAIDw9H//79kZCQgCVLlmDXrl1oamqCSqVCUFAQSktLTVqus7MzEhMTsWbNGmi1WgghsGbNmvviqYjU/nhXZCIikhwPixERkeQYLkREJDmGCxERSY7hQkREkmO4EBGR5BguREQkOYYLERFJjuFCRESS+3+Dft9nug8EFAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "med_incs = [   x[0] for x in  houses.data     ]\n",
    "mean = np.mean(med_incs)\n",
    "sd = np.std(med_incs)\n",
    "\n",
    "\n",
    "sns.distplot(med_incs, bins=20, kde=False)\n",
    "\n",
    "# plt.xlim(-60, 60)\n",
    "\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Median Income');\n",
    "plt.title(\"Histogram of Median Incomes\")\n",
    "sns.despine(offset=10, trim=True);  # move axes away \n",
    "\n",
    "# plot the SD line \n",
    "x_c, y_c = ([mean, mean], [0, 4000])\n",
    "plt.plot(x_c, y_c, color='green', linewidth=2)\n",
    "\n",
    "x_c, y_c = ([mean + sd, mean + sd], [0, 4000])\n",
    "plt.plot(x_c, y_c, color='red', linewidth=2)\n",
    "\n",
    "\n",
    "x_c, y_c = ([mean - sd, mean - sd], [0, 4000])\n",
    "plt.plot(x_c, y_c, color='red', linewidth=2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}