06_module.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Mean"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is a measure of central tendency that is obtained by taking the sum of values diving  by the total number of values in the distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "distribution = [0,2,3,3,3,4,13]\n",
    "mean = sum(distribution) / len(distribution)\n",
    "center = False\n",
    "\n",
    "above = []\n",
    "below = []\n",
    "\n",
    "for value in distribution:\n",
    "    if value < mean:\n",
    "        below.append(mean - value)\n",
    "    if value > mean:\n",
    "        above.append(value - mean)\n",
    "        \n",
    "equal_distances = (sum(above) == sum(below))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equal_distances"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From above, we can think of the mean as the value located at that particular point in the distribution where the total distance of the values below the mean is the same as the total distance of the values that are above the mean."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Task\n",
    "\n",
    "Generate 5000 different distributions, measure the total distances above and below the mean, and check whether they are equal. For each of the 5000 iterations of a for loop:\n",
    "\n",
    "+ Set a seed using the seed() function from numpy.random. For the first iteration, the seed number should be 0, for the second iteration it should be 1, for the third it should be 2, and so on.\n",
    "+ Generate randomly a distribution of integers using the `randint()` function from numpy.random. Pass the right arguments to randint() such that each distribution will:\n",
    "\n",
    "        + Have 10 values.\n",
    "        + The values can range from 0 to 1000.\n",
    "+ Compute the mean of the distribution.\n",
    "+ Measure the total distance above and below the mean.\n",
    "\n",
    "       + Round off each distance to 1 decimal place using the `round()` function. This will prevent rounding errors at the 13th or 14th decimal place.\n",
    "+ Compare the two sums. If they are equal, then increment a variable named equal_distances with 1. You'll need to define equal_distances outside the loop with a value of 0.\n",
    "\n",
    "At the end equal_distances should have a value of 5000. This will confirm that for each of the 5000 distributions the total distance of the values above the mean is equal to the total distance of the values below the mean.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randint, seed\n",
    "equal_distances = 0\n",
    "\n",
    "for i in range(5000):\n",
    "    seed(i)\n",
    "    distribution = randint(0,1000,10)\n",
    "    mean = sum(distribution) / len(distribution)\n",
    "    \n",
    "    above = []\n",
    "    below = []\n",
    "    for value in distribution:\n",
    "        if value == mean:\n",
    "            continue # continue with the next iteration because the distance is 0\n",
    "        if value < mean:\n",
    "            below.append(mean - value)\n",
    "        if value > mean:\n",
    "            above.append(value - mean)\n",
    "    \n",
    "    sum_above = round(sum(above),1)\n",
    "    sum_below = round(sum(below),1)\n",
    "    if (sum_above == sum_below):\n",
    "        equal_distances += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5000"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equal_distances"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating a function for calculating mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "distribution_1 = [42, 24, 32, 11]\n",
    "distribution_2 = [102, 32, 74, 15, 38, 45, 22]\n",
    "distribution_3 = [3, 12, 7, 2, 15, 1, 21]\n",
    "def mean(distribution):\n",
    "    sum_distribution = 0\n",
    "    for value in distribution:\n",
    "        sum_distribution += value\n",
    "        \n",
    "    return sum_distribution / len(distribution)\n",
    "\n",
    "mean_1 = mean(distribution_1)\n",
    "mean_2 = mean(distribution_2)\n",
    "mean_3 = mean(distribution_3)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introducing the dataset\n",
    "\n",
    "We'll be working with a data set that describes characteristics of houses sold between 2006 and 2010 in the city of Ames (located in the American state of Iowa). There are 2930 rows in the data set, and each row describes a house. For each house there are 82 characteristics described, which means there are 82 columns in the data set. \n",
    "\n",
    "A paper which describes the dataset [Ames Housing Dataset Details](data/Ames%20Iowa%20Alternative%20to%20the%20Boston%20Housing%20Data%20as%20an%20End%20of%20Semester%20Regression%20Project.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "houses = pd.read_table('data/AmesHousing_1.txt')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Distribution of sales prices of houses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count      2930.000000\n",
       "mean     180796.060068\n",
       "std       79886.692357\n",
       "min       12789.000000\n",
       "25%      129500.000000\n",
       "50%      160000.000000\n",
       "75%      213500.000000\n",
       "max      755000.000000\n",
       "Name: SalePrice, dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['SalePrice'].describe()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the distribution has a large range: the minimum sale price is $12789 while the maximum is $755000. Among this diversity of prices, we can see that the mean (or the \"balance point\") of this distribution is approximately $180796. The mean gives us a sense about the typical sale price in this distribution of 2930 prices."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating just the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "180796.0600682594"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['SalePrice'].mean()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing means calculated by two different ways"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean(distribution):\n",
    "    sum_distribution = 0\n",
    "    for value in distribution:\n",
    "        sum_distribution += value\n",
    "        \n",
    "    return sum_distribution / len(distribution)\n",
    "function_mean = mean(houses['SalePrice'])\n",
    "pandas_mean = houses['SalePrice'].mean()\n",
    "means_are_equal = (function_mean == pandas_mean)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating population mean\n",
    "\n",
    "In the exercise below, we'll try to visualize on a scatter plot how the sampling error changes as we increase the sample size. Just to prove a point, we'll assume that our data set describes all the houses sold in Ames, Iowa between 2006 and 2010.\n",
    "\n",
    "#### Instructions\n",
    "\n",
    "\n",
    "\n",
    "1. Compute the mean of the SalePrice variable. We'll assume that the data we have is a population relative to the question \"What's the mean sale price of a house in Ames, Iowa for the period 2006-2010?\".\n",
    "\n",
    "2. For each iteration of a for loop that iterates 101 times:\n",
    "\n",
    "  + Sample the SalePrice distribution using the Series.sample() method.\n",
    "\n",
    "    + For the first iteration, the random_state parameter is 0, for the second iteration is 1, for the third is 2, and so on.\n",
    "    + For the first iteration, the sample size is 5.\n",
    "    + The last sample size is 2905 (which is close to 2930, the population's size).\n",
    "    + To achieve that, you'll need to increment the sample size by 29 for every new iteration. Note that you'll first have to define the sample size with a value of 5 outside the loop.\n",
    "    \n",
    " + Compute the sample mean.\n",
    " + Compute the sampling error. For answer checking purposes, use parameter−statistic, not statistic−parameter\n",
    "\n",
    "3. Generate a scatter plot to represent visually how the sampling error changes as the sample size increases.\n",
    "\n",
    "+ Place the sample sizes on the x-axis.\n",
    "+ Place the sampling errors on the y-axis.\n",
    "+ Use `plt.axhline()` to generate a horizontal line at 0 to illustrate the point where the sampling error is 0.\n",
    "+ Use `plt.axvline()` to generate a vertical line at 2930 to illustrate the population size.\n",
    "+ Label the x-axis \"Sample size\".\n",
    "+ Label the y-axis \"Sampling error\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sampling error')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fBlokKXc3DVM4EBER/Q8DLSIbcE9HIiKyBAMtIitxT0ciIrIUJ8MTWYF7OhIRkTUYaBFZqL49HYGqPR0rKrnZAhERVWGgRapQUSkg8+RlfJl9HpknLzskmLFmT0ciIiKAc7RIBZQyJ6rwWu1Bli3liIjI+bFHixRNSXOiuKcjERFZi4EWKZbS5kRxT0ciIrIWAy1SLKXNieKejkREZC0GWqRYSpwTxT0diYjIGpwMT4ql1DlR3NORiIgsxUCLFMs4J6rAcMvsPC0NqnqSHDEnins6EhGRJTh0SIrFOVFERKR2DLRI0TgnioiI1IxDh6R4nBNFRERqxUCLVIFzooiISI04dEhEREQkEwZaRERERDLh0KGKVFQKnKdERESkIgy0VCI1Jx/ztuSabEkTqvPCnCGRXHlHRESkUBw6VIHUnHxM3HCwxr5/BYZbmLjhIFJz8h1UMyIiIqoLAy2Fq6gUMG9LrtnM6MZj87bkoqLSXAkiIiJyJAZaCrcv70qNnqzbCQDyDbewL++K/SpFREREFmGgpXCF12oPsmwpR0RERPbDQEvhgv286i9kRTkiIiKyH646VLiuEYEI1XmhwHDL7DwtDar2/esaEWjvqtmMaSqIiMhVMNBSOHc3DeYMicTEDQehAUyCLWNoMmdIpGoCFaapICIiV8KhQxWIjwrFytGdodeZDg/qdV5YObqzagIUpqkgIiJXwx4tlYiPCkX/SL1qh9zqS1OhQVWaiv6RetW8JyIiovow0FIRdzcNYto0cXQ1bGJNmgq1vkciIqLqVDt0uGjRImg0GiQlJYnHBEHA3LlzERYWBm9vb/Tq1QtHjx41eVxJSQmmTJmCoKAg+Pr6YujQofj9999NyhQVFWHMmDHQ6XTQ6XQYM2YMrl69aod35bzUnqaiolJA5snL+DL7PDJPXmaCWCIisogqA639+/fj3Xffxb333mty/PXXX0dKSgpWrFiB/fv3Q6/Xo3///rh27ZpYJikpCZs3b8amTZuQkZGBP//8E4MHD0ZFRYVYZuTIkcjOzkZqaipSU1ORnZ2NMWPG2O39OSM1p6lIzclHz8U7MGL1HkzblI0Rq/eg5+IdnFNGRET1Ul2g9eeff2LUqFFYvXo1AgICxOOCIGDZsmV44YUXMHz4cERFRWH9+vW4ceMGPvroIwCAwWDAmjVrsGTJEvTr1w+dOnXChg0bcOTIEXz33XcAgGPHjiE1NRXvvfceYmJiEBMTg9WrV+Prr7/G8ePHzdappKQExcXFJjcyZUxTUdvsKw2qVh8qLU0FJ/ATEVFDqC7QeuaZZzBo0CD069fP5HheXh4KCgowYMAA8ZhWq0VsbCx2794NAMjKykJZWZlJmbCwMERFRYllMjMzodPp0K1bN7FM9+7dodPpxDLVLVq0SBxm1Ol0CA8Pl+z9OgtjmgoANYItpaap4D6TRETUUKoKtDZt2oSDBw9i0aJFNe4rKCgAAISEhJgcDwkJEe8rKCiAp6enSU+YuTLBwcE1nj84OFgsU11ycjIMBoN4O3funPVvzgWoLU2FPfaZ5NwvIiLnZtWqw4qKCmRkZODee++tEazI7dy5c5g2bRrS0tLg5VX7PB6NxrRHRBCEGseqq17GXPm6nker1UKr1db5GlRFTWkq5J7Az+StRETOz6oeLXd3d8TFxTlkBV5WVhYKCwsRHR2NRo0aoVGjRkhPT8dbb72FRo0aiT1Z1XudCgsLxfv0ej1KS0tRVFRUZ5mLFy/WeP0//vijRm8Z2caYpmJYx2aIadNEkUEWIO8Efs79IiJyDVYPHXbo0AGnTp2Soy516tu3L44cOYLs7Gzx1qVLF4waNQrZ2dlo3bo19Ho9tm/fLj6mtLQU6enp6NGjBwAgOjoaHh4eJmXy8/ORk5MjlomJiYHBYMC+ffvEMnv37oXBYBDLkGuQawI/534REbkOqxOWLliwALNmzcIrr7yC6Oho+Pr6mtzv7+8vWeVu5+fnh6ioKJNjvr6+aNKkiXg8KSkJCxcuRNu2bdG2bVssXLgQPj4+GDlyJABAp9Nh3LhxmDlzJpo0aYLAwEDMmjULHTp0ECfXt2/fHvHx8UhMTMQ777wDAPjHP/6BwYMHo127drK8N1ImufaZZPJWIiLXYXWgFR8fDwAYOnSoyZwl4xym2/NR2dvs2bNx8+ZNTJo0CUVFRejWrRvS0tLg5+cnllm6dCkaNWqExx57DDdv3kTfvn2xbt06uLu7i2U2btyIqVOniqsThw4dihUrVtj9/ZDjGSfwV59LpW/AXCq1J28lIiLLaQRBsGp8Ij09vc77Y2NjG1QhZ1BcXAydTgeDwSBbDx/ZV0WlINkE/syTlzFi9Z56y32c2J09WkRE9bhRWo7Il7cBAHLnx8HH0/bdBeX4/ra6NgykyBVJuc+kce5XgeGW2XlaGlT1mCkteSsREVnPprDv6tWrWLNmDY4dOwaNRoPIyEg89dRT0Ol0UtePyOnINfeLiIiUx+pVhwcOHECbNm2wdOlSXLlyBZcuXUJKSgratGmDgwcPylFHIqejtuStRERkG6t7tKZPn46hQ4di9erVaNSo6uHl5eV4+umnkZSUhB9//FHyShI5IzUlbyUiIttYHWgdOHDAJMgCgEaNGmH27Nno0qWLpJUjcnZSzv0iIiLlsXro0N/fH2fPnq1x/Ny5cyZpFIiIiIhcndU9Wo8//jjGjRuHN998Ez169IBGo0FGRgb++c9/YsSIEXLUkRxAynQGRERErsrqQOvNN9+ERqPBk08+ifLycgCAh4cHJk6ciNdee03yCpL9cbNjIiIiaVg1dFhRUYHMzEzMmTMHRUVFyM7OxqFDh3DlyhUsXboUWq1WrnqSnXCzYyIiIulYFWi5u7sjLi4OBoMBPj4+6NChA+699174+PjIVT+yI252TEREJC2rJ8N36NABp06dkqMu5GDWbHZMRERE9bM60FqwYAFmzZqFr7/+Gvn5+SguLja5kXpxs2MiIiJpWT0ZPj4+HgAwdOhQaDR/rUITBAEajQYVFRXS1Y7sKtjPq/5CVpQjIiJydVYHWjt37pSjHqQA3OyYiIhIWlYFWmVlZZg7dy7eeecd3HXXXXLViRyEmx0TmWI+OSJqKKsCLQ8PD+Tk5JgMGZJzMW52XD2Plp55tMjFMJ8cEUnB6qHDJ598EmvWrGFyUifGzY7J1RnzyVUfQjfmk1s5ujODLSKyiNWBVmlpKd577z1s374dXbp0ga+vr8n9KSkpklWOHIebHZOrqi+fnAZV+eT6R+r544OI6mV1oJWTk4POnTsDAE6cOGFyH4cUiUjtrMknxx8jRFQfrjokcgKctC0dpeST4/8pkXOwOtAy+u2333Dy5Ek89NBD8Pb2FvNoEZF9cdK2tJSQT47/p0TOw+rM8JcvX0bfvn1x1113YeDAgcjPr9pk+Omnn8bMmTMlryAR1Y6bgEvPmE+utp+NGlQFPXLlk+P/KZFzsTrQmj59Ojw8PHD27FmTzaQff/xxpKamSlo5IqodNwGXhzGfHIAawZbc+eT4f0rkfKwOtNLS0rB48WI0b97c5Hjbtm1x5swZySpGRHXjJuDyMeaT0+tMhwf1Oi9ZUzvw/5TI+Vg9R+v69esmPVlGly5dglarlaRSRFQ/pUzadlaOyCfH/1Mi52N1j9ZDDz2EDz74QPxbo9GgsrISb7zxBnr37i1p5YiodkqYtO3sjPnkhnVshpg2TWRf9cf/UyLnY3WP1htvvIFevXrhwIEDKC0txezZs3H06FFcuXIFu3btkqOORGQGNwF3Pvw/JXI+VvdoRUZG4vDhw+jatSv69++P69evY/jw4Th06BDatGkjRx2JyAxHTtomefD/lMj5aARB4PIViRUXF0On08FgMMDf39/R1SEnx5xLzof/p0SWu1FajsiXtwEAcufHwcfT5hShsnx/214bIlIESydtKy3TuNLqoyTc2J3IeTDQInIC9W0CrrQeEqXVR4m4sTuRc7B6jhYROV5FpYDMk5fxZfZ5ZJ68XGcCS6VlGldafYiI5MQeLSKVsaY3qL5M4xpUZRrvH6m3y7CU0upDRCQ39mgRqYi1vUFKyzSutPoQEcnN6h6tTp06QaOp+UtTo9HAy8sLd955JxISEpi8lEhitvQGKS3TuNLqQ0QkN6t7tOLj43Hq1Cn4+vqid+/e6NWrFxo3boyTJ0/i/vvvR35+Pvr164cvv/xSjvqSlayZy0PKZktvkNIyjSutPkREcrM60Lp06RJmzpyJn376CUuWLEFKSgp+/PFHzJo1C9evX0daWhpefPFFvPLKK5JWdNGiRbj//vvh5+eH4OBgPPLIIzh+/LhJGUEQMHfuXISFhcHb2xu9evXC0aNHTcqUlJRgypQpCAoKgq+vL4YOHYrff//dpExRURHGjBkDnU4HnU6HMWPG4OrVq5K+H3tIzclHz8U7MGL1HkzblI0Rq/eg5+IdnGysUrb0Bhkzjdc220mDqvld9so0rrT6EBHJzepA65NPPsGIESNqHH/iiSfwySefAABGjBhRIwhqqPT0dDzzzDPYs2cPtm/fjvLycgwYMADXr18Xy7z++utISUnBihUrsH//fuj1evTv3x/Xrl0TyyQlJWHz5s3YtGkTMjIy8Oeff2Lw4MGoqKgQy4wcORLZ2dlITU1FamoqsrOzMWbMGEnfj9y4ssv52NIbpLRM41LUh720RKQmVs/R8vLywu7du3HnnXeaHN+9eze8vKo+4CsrK6HVaqWp4f+kpqaa/L127VoEBwcjKysLDz30EARBwLJly/DCCy9g+PDhAID169cjJCQEH330EcaPHw+DwYA1a9bgww8/RL9+/QAAGzZsQHh4OL777jvExcXh2LFjSE1NxZ49e9CtWzcAwOrVqxETE4Pjx4+jXbt2NepWUlKCkpIS8e/i4mJJ37u1uLLLOdm6D158VChWju5cY6Wi3kF5qxpSH+bfIiK1sTrQmjJlCiZMmICsrCzcf//90Gg02LdvH9577z08//zzAIBt27ahU6dOklf2dgaDAQAQGFj1pZKXl4eCggIMGDBALKPVahEbG4vdu3dj/PjxyMrKQllZmUmZsLAwREVFYffu3YiLi0NmZiZ0Op0YZAFA9+7dodPpsHv3brOB1qJFizBv3jy53qrVrJnLw4SI6mHsDZq44SA0gEmwVV9vkNIyjdtSH2MvbfUg09hLu3J0ZwZbRKQ4VgdaL774IiIiIrBixQp8+OGHAIB27dph9erVGDlyJABgwoQJmDhxorQ1vY0gCJgxYwZ69uyJqKgoAEBBQQEAICQkxKRsSEgIzpw5I5bx9PREQEBAjTLGxxcUFCA4OLjGawYHB4tlqktOTsaMGTPEv4uLixEeHm7ju2s4ruxyXg3pDVJapnFr6qOUXlpuG0RE1rIpYemoUaMwatSoWu/39va2uUKWmDx5Mg4fPoyMjIwa91VPPSEIgtl0FHWVMVe+rufRarWSD5U2BFd2NYzSv0yV1jslpdraXgm9tBy2JCJb2JwZvrS0FIWFhaisrDQ53qJFiwZXqi5TpkzBV199hR9//BHNmzcXj+v1egBVPVKhoX996BUWFoq9XHq9HqWlpSgqKjLp1SosLESPHj3EMhcvXqzxun/88UeN3jKlsnUuD6nny1RpvVNSqKvtS8or63jkX+TqpVXKsKXSfwQQUU1Wrzr89ddf8eCDD8Lb2xstW7ZEREQEIiIi0KpVK0RERMhRRwBVPUqTJ0/GF198gR07dtR4rYiICOj1emzfvl08VlpaivT0dDGIio6OhoeHh0mZ/Px85OTkiGViYmJgMBiwb98+sczevXthMBjEMkqntJVmasGVmo5TX9ufvnS9lkeakqOXtr5hS6Bq2FLu1Y9M10KkTlb3aCUkJKBRo0b4+uuvERoaWu+wnFSeeeYZfPTRR/jyyy/h5+cnzpfS6XTw9vaGRqNBUlISFi5ciLZt26Jt27ZYuHAhfHx8xLljOp0O48aNw8yZM9GkSRMEBgZi1qxZ6NChg7gKsX379oiPj0diYiLeeecdAMA//vEPDB482OxEeKVS2kozpVPKHCBnVltvjCVt//G+s9D7e+Fisf17aZUybKmEHjUisp7VgVZ2djaysrJw9913y1GfWq1cuRIA0KtXL5Pja9euRUJCAgBg9uzZuHnzJiZNmoSioiJ069YNaWlp8PPzE8svXboUjRo1wmOPPYabN2+ib9++WLduHdzd3cUyGzduxNSpU8XViUOHDsWKFSvkfYMycOa5PFJTwpepM6trWFDn7Vlv2xcUl2B6v7uw7LsTVq+4BBo25OboxSVK/hHAoUyi+lkdaEVGRuLSpUty1KVOglB/t7xGo8HcuXMxd+7cWst4eXlh+fLlWL58ea1lAgMDsWHDBluqqTjOOJdHDo7+MnVm9fXGPPVAK4uep1WQj029tA2dd+foxSVK/RGglvmMRI5mdaC1ePFizJ49GwsXLkSHDh3g4eFhcr+/v79klSOyF0d/mTorS3pjNmeft+i5gv28ENOmiVW9tFIMuTl6cYkSfwS44lAme+/IVlYHWsa5TH379jU5bkx/cPtWNkRq4egvU2dlSW/MletlCPT1RNH1Uova3tJeWqmG3BqSKFYKSvsRoOShTLmw944awupAa+fOnXLUg8ihHP1lWhc1/5K2tJflkY5hWLvrtKRtL+WQmyMXlyjtR4BShzLl4oq9dyQtqwOt2NhYOepB5HBKXKmp9l/Slvay9I/Uo2tEoKRtL/WQm6MWl9T1IwD/+3tgVFW97FEfJQ5lysUVe+9IehYFWocPH0ZUVBTc3Nxw+PDhOsvee++9klSMyBGUtFJTqb+krelhs6Y3xt1NI2nbyzHk5qjFJbX9CHDTAJUCsGbXaazZddouQbjShjLl5Gq9dyQPiwKtjh07insAduzYERqNxuwqQM7RImeghJWaSv0lbW0Pm7VDslK2vdKG3Brq9h8B23ML8P6u06ieI9UeQbiztWtdXKn3juRjUWb4vLw8NG3aVPz3qVOnkJeXV+N26tQpWStL5Cqs+SVtL7Zmzjf2xuh1pj0cep2XrAGBvXZIqKgUkHnyMr7MPo/Mk5dlzRDv7qZB14hAfJtjfoN7e2Sqd6WdJ1yp947kY1GPVsuWLc3+m4jkobRf0g3tYXPUkKzc8+4cMYdOCcNZSpzPKAdX6r0j+VgUaH311VcWP+HQoUNtrgypi5pXwymd0n5JW/rlvnT7CTxwZ5DZc8GR85vkCPIcNYdOKUF4Q9pVLZ8dSl6NTOphUaD1yCOPWPRknKPlOtS+Gk7plPZL2tIv7RU7f8OKnb8p7lyQOshz5Bw6JQXhtrSr2j47XKX3juRj0RytyspKi24MslyDrXN1yHJKmwdj7Ze2s58LjpxDZwzCa/uf16AqcFHicJZaPzvio0KR8WwffJzYHf96oiM+TuyOjGf7MMgii1gUaBEZ1fdLHpB3Iq4rcdQkcnPq+3KvztnPBUcO3yktCLeU2j87jL13wzo2Q0ybJoprX1IumwKt77//HoMHD0abNm1w5513YvDgwfjuu++krhspkBJXwzkzpfySruvLvTbOfC44evhOSUG4pfjZQa7K6szwK1aswPTp0/F///d/mDZtGgBgz549GDhwIFJSUjB58mTJK0nKoZSJuK5ECXm9gNrnqtTHGc8FJcyhU1JyXUvws4NcldWB1qJFi7B06VKTgGrq1Kl44IEHsGDBAgZaTs7Rv+SVTC0rqRri9i/3Xb/9gRU7T9b7mEvXSlBRKThVW1i7Gk2uc0MpQbgl+NlBrsrqQKu4uBjx8fE1jg8YMADPPvusJJUi5VLCL3klUttKqoYwfrl3jQjE5wfP13ouGL2y9Rjey8iTrS0cFeBauhrNlc6NuvCzg1yV1XO0hg4dis2bN9c4/uWXX2LIkCGSVIqUS60TceWk1pVUDWXNvC252iI1Jx89F+/AiNV7MG1TNkas3oOei3fYrc3rm0PnqueGOfWdL7dvjq3UCfFKYs8dCahhNIK5TQvr8Oqrr+LNN9/EAw88gJiYGABVc7R27dqFmTNnwt/fXyw7depUaWurEsXFxdDpdDAYDCbt4Uz4K71KRaWAnot31DpnyfgrPePZPk4bfJo7F8yRui1qSxhqfGZHTwrnuWGeufPFuDm2kSt+lliDn7+mbpSWI/LlbQCA3Plx8PG0erBOJMf3t9WBVkREhGVPrNG47N6HrhBoAa4xJ6k+mScvY8TqPfWW+zixu2rm0tiiolLAul15eGXrsXrLStEWaghieG7UzvjZYdwcuzqlBMtKpPQfGI6g9EDL6trk5eVJ8sKkfmqaiCsXrqSq4u6mQZCf1qKyUrSFEvb7q49Szg0l/iAybo4945Nss/fLnV1frRy5IwHZzvawj4i4kuo29mwLpQQxdVHCuaHkISY1BMtKwzZTJ6sDLUEQ8Nlnn2Hnzp0oLCxEZWWlyf1ffPGFZJUjUjqupPqLPdtCCUFMfRx9bjhq02tLqSFYVhq2mTpZvepw2rRpGDNmDPLy8tC4cWPodDqTG5ErcbZVmA1ZyWTPtlDDfn+OPDfUsN2NGoLlujhi1Z/a28xVWd2jtWHDBnzxxRcYOHCgHPUhUh1L8ykpnRTDTPZqC2sThjqKo84NNQwxObrHryEcNSSr5jZzZVYHWjqdDq1bt5ajLkSqZel2KEqcmAxIO8xkr61h1BLgOmKrHDUMMdUXLAsAnrg/HF8fvuC014q11PIDg0xZnd5h/fr1SE1Nxfvvvw9vb2+56qVqrpLegayj1InJakiVUBelBq+OpKbUEuauizt8PAAAV2+Uicd4rfzF0s8SV7k2nC69w9/+9jd8/PHHCA4ORqtWreDh4WFy/8GDByWpGJEzUfLEZDUMM9WFaUZqUtMQU/Uev9OXbmDZdyd4rdTBkl5Spf6wc0VWB1oJCQnIysrC6NGjERISAo3G+aJjIikpPfeNGoaZyDpqG2IyBsvGHiNeK/Wr6weGkn/YuSKrA62tW7di27Zt6Nmzpxz1IXI6SvkVXBuuZHJOapnDdjt7XCsNGU5Tw7Wi9B92rsjqQCs8PJzzjoisoKRfweaoaZiJrOOIifgNIfe10tDhNDVcK9YGq/acx+Uqc8aqszrQWrJkCWbPno1Vq1ahVatWMlSJ7M1VT357UfqvYLUNMzkDc9ccAEmuQ3PPrZY5bHJeK1IMp6nhWrE0CN312x8oul6KV7baZx6XK0/gtzrQGj16NG7cuIE2bdrAx8enxmT4K1euSFY5kh8nTMpPDb+C1TjMpFZyrrJT+/Us17Ui5XCa0q8VS4PQFTtPmj0uxzwuS4NctZ+/tbEpvUNdxo4d26AKOQO1pHdwxV3gHfVrydjWgPlfwUppa2f8NakktV1z5lh7bjjL9SzHtSJHugtLrhVHXE/GBQW1BauWkDJNhaUpMV4aFIlnPrLt/HW69A4MpJyDK06YdOSvJaX/CjZiqgT51HXNmWPNdajk69naYEOOa0WOuV/1XSuO+rypa3jTUlIu0LF0ztiLX+Yo8vyVgu1hH4CbN2+irKzM5JiSe3DoL0pfCSc1JSx3VtvEZJJWfdecOZZeh0q9nm0NNqS+Vuw9T9LRnze1BavWasgCHWOA/W1OvkXlr1wvrfU+tX8fWb2p9PXr1zF58mQEBwejcePGCAgIMLk5k3//+9+IiIiAl5cXoqOj8dNPPzm6SpJR+ko4KSlpg13jr+BhHZshpk0TBlkupCHXUn2PVeL1bAw2qn/RG4ON1Hq+gKW8Vuy5CblSPm/io0KR8WwfTO59p83PYWvgmZqTj56Ld2DE6j34IPOMza9fnfH8dcSG3g1hdaA1e/Zs7NixA//+97+h1Wrx3nvvYd68eQgLC8MHH3wgRx0d4j//+Q+SkpLwwgsv4NChQ3jwwQfx8MMP4+zZs46umiSUvhLOEpZebNb82ieSS0OupfoeK8f13JAvM6UEG0bG4TQANYItqVcLKunzxt1NgwfuDLL6cdUDz+rnQml5Za3nRm0BthSC/bxMgrhpm7IxYvUe9EtJl/y1pGT10OGWLVvwwQcfoFevXnjqqafw4IMP4s4770TLli2xceNGjBo1So562l1KSgrGjRuHp59+GgCwbNkybNu2DStXrsSiRYsseo4bpeVoVFouZzVtFtXMHyH+WlwsLqm1TIi/FlHN/HFDge9he24BFn7zi0n9Q/y1eH7g3egfqTcpe67oukXPea7oOu4r1UlaTyIjS645cyy5DqW+nq25vszZe8qyYOPHE3+gW2v7rLZ96K6mWPbEfTXeV/D/3tdDdzWV5LPO2s+bikoBB04X4Y8/b6FpYy90aRUgaU+3LeedAOC5h9uhpLzC7LlQfe6X8dzoc3cI5nx11OZJ+HUJ8deiwHAT0z/5ucZ9t9etof+HcnzfWb3qsHHjxjh69ChatmyJ5s2b44svvkDXrl2Rl5eHDh064M8//5S8kvZWWloKHx8ffPrpp/h//+//icenTZuG7OxspKebRs8lJSUoKfnrP7q4uBjh4eEIT/oEblofu9WbiIiIbFdZcgPnlj0m6apDq4cOW7dujdOnTwMAIiMj8cknnwCo6um64447JKmUo126dAkVFRUICQkxOR4SEoKCgoIa5RctWgSdTifewsPD7VVVIiIiUjCrhw7//ve/4+eff0ZsbCySk5MxaNAgLF++HOXl5UhJSZGjjg5TfcNsQRDMbqKdnJyMGTNmiH8be7T2vdBXFasw5e66ltLeU1fw93X76y23NuF+kyGJ7bkFmLapZpez0b+euM+iIREiKZi75gBIch1acj3XVsbW68tcHfqlpNc7lPndjFi75JWy9+dbfZ83k3q1xsY9Z2G4VfswlbF9dvxysc5hXGs+26xpC0vPBbmM6BqOAZF6sY5fH76A2Z8dqfdxrz5yD4Z3bm7z6xYXFyN0mc0PN8vqQGv69Oniv3v37o1jx44hKysLbdq0wX333Sdp5RwlKCgI7u7uNXqvCgsLa/RyAYBWq4VWq61x3MezUYMSp9lT77uDHV0FixTfKqu/0P/K3d72wzo2h7aRu1NmHSbbODo5q7lrTqrrsK7nqSvlQkl5pUXPX/36Mmfe0HvqTDw6b+g98PPyqPE4KTkql1VtnzfGHQD+/cOpep/jYnEJ3s84jWXfnagx56mwuARJm37G2yPd8Nq3x2t9Dg2A1749jsH3NhPPbUvPMUs/a6u7w9sDhptltWb2D/D1wJXr9T/30PuamezFePbyDYtev9kdPg363i2X4Tu7wc/YsmVLtGzZUoq6KIanpyeio6Oxfft2kzla27dvx7BhwxxYM2rI6irmsSIjZ93qoz515XeasOEg/q9zM4uex5Lr0NFJepWQy+r2z5vTl26YDZrqsnZXXp1JPF/8MqfOoKUh+adsXSX79wcisOy7E7XuBfnqsCi8svWYRdssmbtO62PsHVYSiwOtvXv34sqVK3j44YfFYx988AHmzJmD69ev45FHHsHy5cvN9uyo0YwZMzBmzBh06dIFMTExePfdd3H27FlMmDDB0VVzaQ3dC42Zz8nRX8COYknKhc8Onq/zOazda9BRP26Ukinf+Hlj3IbG2tV4V2/WHURZ0jMEWJc/zdiDVGC4iUBfTxRdL7V4yyi9zguT+9yJdvrGdQbYbm6aejfm3p5bYPF2VbdT4g9niwOtuXPnolevXmKgdeTIEYwbNw4JCQlo37493njjDYSFhWHu3Lly1dWuHn/8cVy+fBnz589Hfn4+oqKi8M033zhd753a1LW9hNT5cMj5KOUL2BFsyUx/O1uvL0f8uLE2U77cw8jWtr0GgM7bo85AyxqW9k7Z0oME1Dw36guw6+vt7B+ptyowtSVtij1ZHGhlZ2fjlVdeEf/etGkTunXrhtWrVwMAwsPDMWfOHKcJtABg0qRJmDRpkqOrQdU4ekiC1EupW9XYQ0Ozwldt/NseOm9PfJl9XtFD79ZkyrfHMLI1bW9szb8/0ApLv/u13vJ19TpZ0wNpzYbnbhrg9lyz5j576wuw6wrGMk9etijYm9z7TjxwZxCimvmjw9w0C2ruGBYHWkVFRSYTwdPT0xEfHy/+ff/99+PcuXPS1o6s5ugJvvbC+VZkCyVuVWMvDclM/9Kg9gjVeeOVrcqa11bb552l77W2eVNSDyNb0/a39+ps2n+u3mkSLw2KxDMfNayH35INzwN9PfDS4Hug9/dCdMsAZJ0pavBnb23BmKXXX9uQxohp00SRSbVvZ3GgFRISgry8PISHh6O0tBQHDx7EvHnzxPuvXbsGDw95V5BQ3Vxtgi/nW5G1nGHrKVvVN7+xLuev3sSrW48pal5bXZ93/SP19c7lDPHX4uN9Z+0yjGxJ29/h7YG3R3VG99Z/7etoyTSJ+KhQrHRrWA+/JUObV66XQe/vJX7myvnZ62zXqcUJS+Pj4/Hcc8/hp59+QnJyMnx8fPDggw+K9x8+fBht2rSRpZJUv4Zu4ErkCuyxubBSN7yta7+/+vw3+4Ji9i0E6v+8255bUO/ehiO6tkBBsX32JKxvr0UNgNce7YAH7gwyCeqM0yT0OtOAQq/zMglujRtIf5zYHf96oiM+TuyOjGf7WBz8StHTK+V5b89NwO3B4h6tV199FcOHD0dsbCwaN26M9evXw9PTU7z//fffx4ABA2SpJNXNlSf4EllD7sUUSu9Vrm1+Y23+yntUWmsZe89rs/TzLuPZPnXO5bQ0Z5hUw8i2zi21dJpEQ3r4G9qDJPV572yLniwOtJo2bYqffvoJBoMBjRs3hru7u8n9n376KRo3bix5Bal+rjzBl8haci2mUEvaiNryOwHmv9D+X8dmWLPrdL3Pa695bdZ83tU34doSUg5P2Tq3VO5pEg1JmyPXee9Mi56sTliq0+nMHg8MVEcXnjNy5Qm+RLYw94VnnOBry4o6tfUqV//irivvkc7b06JAy17zZaz9vKstSGloTj5bKXFuqa09SHKf986y6Ekd+8NQnZxt4iCRPdz+hZeak4/YN3baPPSh9l7lur7QKioFhwQktZHq806O4SmpVn07YvW4LT1I9jjvlRiYWouBlhNw1C8zImcgxdCHM/Qq1/aFprT5Mpau4KsUBFRUCnXWS8rhKanmKTlynp+1PUjOcN7bg8WrDkm56lvRAqhr4iCRvViyLY0lK+qcvVfZ0tVv9mDJ6smrN8sw6r296Ll4R70rrhu6Yg+QbtW3ElaPGwPuYR2rNnWu63vD2c97qbBHy0kodeKgqyRQJXWSaujDFXqVLe3tsMc1b+nqSUt7JRsyPCXVPCW1zfMDXOO8lwIDLSeitImDSl/qTiTV0IfShtfkUl9AYs9r3vh5t+fkZTzz0UGz+wLaI0CRKlhX4zw/VznvG4pDh07Gmm5fOSmhC5yoPlIOfShpeM0R5L7mzSXEdHfTwM1NU+fmy1ImHjVHqmBdrfOdXP28twR7tEhyauwCJ9ck9dCH0nqV7UXua76unjJ7Jx6tTqpgXc3znVz1vLcUe7RIctZ0gRM5khwLSZTSq2xPcl7z9fWUnb503aLnkStAkWq7GLVvO+OK572lGGiR5NTaBU6uiUMfDSfXNW/JqtCP952F3t9xAYpUwTpXjzsvDh2S5NTcBU6uiUMfDSPXNW9JT1lBcQmm97sLy7474bAJ2VKt+lbq6nFqGAZaJDku+SU1coYM1I4i1zVvaQ9YqyAfhwcoUgXrDPqdDwMtkhyX/BK5FrmueWt6ymLaNHF4gCJVsM6g37lwjhbJgvNeiFyLHNe8tRPEOSGblIg9WiQbe3eBMws9kWNJfc2zd5ycAQMtkpWtXeDWBk3MQk+kDFIPe3GCOKkdAy1SHGuDJmOeneqTcC3d54yIlI0TxEnNGGiRolgbNDELPZFrsOcEcU5DICkx0CLFsCVoUuNGrESkXJyGQFLjqkNSDFu28WAWeiKSitwbY5NrYqBFimFL0MQs9EQkBUu2+5m3JRcVleZKENWOgRYphi1Bk9o3YiUiZZBzY2xybQy0SDFsCZq4ESsRSYHTEEguDLRIMWwNmpiFnogaitMQSC5cdUiKYmtyQubZIaKGkGtjbCIGWqQ4tgZN3IiViGzF7X5ILgy0SJEYNBGRvXG7H5IDAy0iIqL/4TQEkhoDLSKZcBsPInVijzpJiYEWkQy4jYc0GKwSkdox0CKSmLUbY5N5DFaJyBmoIo/W6dOnMW7cOERERMDb2xtt2rTBnDlzUFpaalLu7NmzGDJkCHx9fREUFISpU6fWKHPkyBHExsbC29sbzZo1w/z58yEIpl+J6enpiI6OhpeXF1q3bo1Vq1bJ/h7JOXAbD2lwzzkichaq6NH65ZdfUFlZiXfeeQd33nkncnJykJiYiOvXr+PNN98EAFRUVGDQoEFo2rQpMjIycPnyZYwdOxaCIGD58uUAgOLiYvTv3x+9e/fG/v37ceLECSQkJMDX1xczZ84EAOTl5WHgwIFITEzEhg0bsGvXLkyaNAlNmzbFo48+6rA2IHWwZhsPzgExr75gVYOqYLV/pJ7DiESkeKoItOLj4xEfHy/+3bp1axw/fhwrV64UA620tDTk5ubi3LlzCAsLAwAsWbIECQkJWLBgAfz9/bFx40bcunUL69atg1arRVRUFE6cOIGUlBTMmDEDGo0Gq1atQosWLbBs2TIAQPv27XHgwAG8+eabDLSoXtzGo+EYrBKRM1HF0KE5BoMBgYF/ZejNzMxEVFSUGGQBQFxcHEpKSpCVlSWWiY2NhVarNSlz4cIFnD59WiwzYMAAk9eKi4vDgQMHUFZWZrYuJSUlKC4uNrmRa+I2Hg3HYJWInIkqA62TJ09i+fLlmDBhgnisoKAAISEhJuUCAgLg6emJgoKCWssY/66vTHl5OS5dumS2PosWLYJOpxNv4eHhDXuDpFq2bIxNphisEpEzcWigNXfuXGg0mjpvBw4cMHnMhQsXEB8fj7/97W94+umnTe7TaGp+vQmCYHK8ehnjRHhry9wuOTkZBoNBvJ07d66+t05OytaNsekvDFaJyJk4dI7W5MmT8cQTT9RZplWrVuK/L1y4gN69eyMmJgbvvvuuSTm9Xo+9e/eaHCsqKkJZWZnYQ6XX68WeK6PCwkIAqLdMo0aN0KSJ+fkgWq3WZDiSXJuzbeNh71xWUuw5x/xbRKQUDg20goKCEBQUZFHZ8+fPo3fv3oiOjsbatWvh5mbaGRcTE4MFCxYgPz8foaFVX2RpaWnQarWIjo4Wyzz//PMoLS2Fp6enWCYsLEwM6GJiYrBlyxaT505LS0OXLl3g4eHRkLdLLkQJ23hIEWw4KpdVQ4JV5t8iIiXRCNWTSCnQhQsXEBsbixYtWuCDDz6Au7u7eJ9erwdQld6hY8eOCAkJwRtvvIErV64gISEBjzzyiJjewWAwoF27dujTpw+ef/55/Prrr0hISMDLL79skt4hKioK48ePR2JiIjIzMzFhwgR8/PHHFq86LC4uhk6ng8FggL+/v8StQVQ/KYKN2hKvGkM1eyRetTZYVEKdici+bpSWI/LlbQCA3Plx8PG0vQ9Jju9vVaR3SEtLw2+//YbffvsNzZs3N7nPGCe6u7tj69atmDRpEh544AF4e3tj5MiRYvoHANDpdNi+fTueeeYZdOnSBQEBAZgxYwZmzJghlomIiMA333yD6dOn4+2330ZYWBjeeustpnYg1ZAiM71ScllZs+ecUupMRHQ7VfRoqQ17tMhRKioF9Fy8o9Y8VBpUDb9lPNunzmAj8+RljFi9p97X+zixu2JyWamxzkTUcErv0VJlegciMs+aZJ91UWMuKzXWmYicHwMtIiciVbChxlxWaqwzETk/BlpETkSqYEONuazUWGcicn4MtIiciFTBhhoTr6qxzkTk/BhokcUqKgVknryML7PPI/PkZVRUch2F0kgZbBhzWel1pr1fep2XYtMkqLHOROTcVJHegRyPSSDVQ8rM9EpIvGotNdaZiJwXAy2qlxR5mci+pAw2rMllpRRqrDMROScGWlQnJoFULwYbRESOxzlaVCep8jIRERG5IgZaVCcmgSQiIrIdAy2qE5NAEhER2Y6BFtWJSSCJiIhsx0CL6sQkkERERLZjoEX1YhJIIiIi2zC9A1mESSCJiIisx0CLLMa8TERERNbh0CERERGRTBhoEREREcmEgRYRERGRTBhoEREREcmEgRYRERGRTLjqkEhhKioFptEgInISDLSIFCQ1Jx/ztuQi3/DXJt2hOi/MGRLJxLBERCrEoUMihUjNycfEDQdNgiwAKDDcwsQNB5Gak++gmhERka0YaBEpQEWlgHlbciGYuc94bN6WXFRUmitBRERKxUCLSAH25V2p0ZN1OwFAvuEW9uVdsV+liIiowRhoESlA4bXagyxbyhERkTIw0CJSgGA/L0nLERGRMjDQIlKArhGBCNV5obYkDhpUrT7sGhFoz2oREVEDMdAiUgB3Nw3mDIkEgBrBlvHvOUMimU+LiEhlGGgRKUR8VChWju4Mvc50eFCv88LK0Z2ZR4uISIWYsJRIQeKjQtE/Us/M8EREToKBFpHCuLtpENOmiaOrQUREEuDQIREREZFMGGgRERERyYSBFhEREZFMVBdolZSUoGPHjtBoNMjOzja57+zZsxgyZAh8fX0RFBSEqVOnorS01KTMkSNHEBsbC29vbzRr1gzz58+HIJjuH5eeno7o6Gh4eXmhdevWWLVqldxvi4iIiJyQ6ibDz549G2FhYfj5559NjldUVGDQoEFo2rQpMjIycPnyZYwdOxaCIGD58uUAgOLiYvTv3x+9e/fG/v37ceLECSQkJMDX1xczZ84EAOTl5WHgwIFITEzEhg0bsGvXLkyaNAlNmzbFo48+avf3Sw1TUSlwBR8RETmMqgKtb7/9Fmlpafj888/x7bffmtyXlpaG3NxcnDt3DmFhYQCAJUuWICEhAQsWLIC/vz82btyIW7duYd26ddBqtYiKisKJEyeQkpKCGTNmQKPRYNWqVWjRogWWLVsGAGjfvj0OHDiAN998k4GWyqTm5GPellyTzZpDdV6YMySSOamIiMguVDN0ePHiRSQmJuLDDz+Ej49PjfszMzMRFRUlBlkAEBcXh5KSEmRlZYllYmNjodVqTcpcuHABp0+fFssMGDDA5Lnj4uJw4MABlJWVma1bSUkJiouLTW7kWKk5+Zi44aBJkAUABYZbmLjhIFJz8h1UMyIiciWqCLQEQUBCQgImTJiALl26mC1TUFCAkJAQk2MBAQHw9PREQUFBrWWMf9dXpry8HJcuXTL72osWLYJOpxNv4eHh1r9JkkxFpYB5W3IhmLnPeGzellxUVJorQUREJB2HBlpz586FRqOp83bgwAEsX74cxcXFSE5OrvP5NJqac28EQTA5Xr2McSK8tWVul5ycDIPBIN7OnTtXZz1JXvvyrtToybqdACDfcAv78q7Yr1JEROSSHDpHa/LkyXjiiSfqLNOqVSu8+uqr2LNnj8mQHwB06dIFo0aNwvr166HX67F3716T+4uKilBWVib2UOn1erHnyqiwsBAA6i3TqFEjNGliPlu3VqutUTdynMJrtQdZtpQjIiKylUMDraCgIAQFBdVb7q233sKrr74q/n3hwgXExcXhP//5D7p16wYAiImJwYIFC5Cfn4/Q0KqJzmlpadBqtYiOjhbLPP/88ygtLYWnp6dYJiwsDK1atRLLbNmyxeT109LS0KVLF3h4eDT4PZP8gv286i9kRTkiIiJbqWKOVosWLRAVFSXe7rrrLgBAmzZt0Lx5cwDAgAEDEBkZiTFjxuDQoUP4/vvvMWvWLCQmJsLf3x8AMHLkSGi1WiQkJCAnJwebN2/GwoULxRWHADBhwgScOXMGM2bMwLFjx/D+++9jzZo1mDVrlmPePFmta0QgQnVeqC2JgwZVqw+7RgQCqJrTlXnyMr7MPo/Mk5c5d4uIiCSjqvQOdXF3d8fWrVsxadIkPPDAA/D29sbIkSPx5ptvimV0Oh22b9+OZ555Bl26dEFAQABmzJiBGTNmiGUiIiLwzTffYPr06Xj77bcRFhaGt956i6kdVMTdTYM5QyIxccNBaACTSfHG4GvOkEi4u2mYAoKIiGSlEaqnRacGKy4uhk6ng8FgEHvTyP7qC6KMKSCqXwDGYGzl6M4MtoiIFO5GaTkiX94GAMidHwcfT9v7kOT4/naaHi2i6uKjQtE/Um82M3x9KSA0qEoB0T9Sz0zyRERkMwZa5NTc3TSIaVNztag1KSDMPZ6IiMgSqpgMTyQ1poAgIiJ7YKBFLokpIIiIyB4YaJFLsjYFBBERkS0YaJFLMqaAAFAj2KqeAoKIiMhWDLTIZcVHhWLl6M7Q60yHB/U6L6Z2ICIiSXDVIbm0ulJAEBERNRQDLXJ5taWAICIiaigOHRIRERHJhIEWERERkUwYaBERERHJhIEWERERkUwYaBERERHJhIEWERERkUyY3sEFVVQKzBtFRERkBwy0XExqTj7mbclFvuGWeCxU54U5QyKZCZ2IiEhiHDp0Iak5+Zi44aBJkAUABYZbmLjhIFJz8h1UMyIiIufEQMtFVFQKmLclF4KZ+4zH5m3JRUWluRJERERkCwZaLmJf3pUaPVm3EwDkG25hX94V+1WKiIjIyTHQchGF12oPsmwpR0RERPXjZHgXEeznJWk5cg5cgUpEJC8GWi6ia0QgQnVeKDDcMjtPSwNAr6v6oiXXwBWoRETy49Chi3B302DOkEgAVUHV7Yx/zxkSyd4MF8EVqERE9sFAy4XER4Vi5ejO0OtMhwf1Oi+sHN2ZvRgugitQiYjsh0OHLiY+KhT9I/Wcl+PCrFmBGtOmif0qRkTkhBhouSB3Nw2/QF0YV6ASEdkPhw6JXAxXoBIR2Q8DLSIXY1yBWttgsQZVqw+5ApWIqOEYaBG5GK5AJSKyHwZaRC6IK1CJiOyDk+GJXBRXoBIRyY+BFpEL4wpUIiJ5ceiQiIiISCYMtIiIiIhkwkCLiIiISCaqCrS2bt2Kbt26wdvbG0FBQRg+fLjJ/WfPnsWQIUPg6+uLoKAgTJ06FaWlpSZljhw5gtjYWHh7e6NZs2aYP38+BMF0T7f09HRER0fDy8sLrVu3xqpVq2R/b0REROR8VDMZ/vPPP0diYiIWLlyIPn36QBAEHDlyRLy/oqICgwYNQtOmTZGRkYHLly9j7NixEAQBy5cvBwAUFxejf//+6N27N/bv348TJ04gISEBvr6+mDlzJgAgLy8PAwcORGJiIjZs2IBdu3Zh0qRJaNq0KR599FGHvHciIiJSJ41QvTtHgcrLy9GqVSvMmzcP48aNM1vm22+/xeDBg3Hu3DmEhYUBADZt2oSEhAQUFhbC398fK1euRHJyMi5evAitVgsAeO2117B8+XL8/vvv0Gg0ePbZZ/HVV1/h2LFj4nNPmDABP//8MzIzM82+dklJCUpKSsS/i4uLER4eDoPBAH9/f6magYiIiKq5UVqOyJe3AQBy58fBx9P2PqTi4mLodDpJv79VMXR48OBBnD9/Hm5ubujUqRNCQ0Px8MMP4+jRo2KZzMxMREVFiUEWAMTFxaGkpARZWVlimdjYWDHIMpa5cOECTp8+LZYZMGCAyevHxcXhwIEDKCsrM1u/RYsWQafTibfw8HCp3joRERGpmCoCrVOnTgEA5s6dixdffBFff/01AgICEBsbiytXrgAACgoKEBISYvK4gIAAeHp6oqCgoNYyxr/rK1NeXo5Lly6ZrV9ycjIMBoN4O3fuXAPfMRERETkDhwZac+fOhUajqfN24MABVFZWAgBeeOEFPProo4iOjsbatWuh0Wjw6aefis+n0dTMaC0Igsnx6mWMI6fWlrmdVquFv7+/yY2IiIjIoZPhJ0+ejCeeeKLOMq1atcK1a9cAAJGRkeJxrVaL1q1b4+zZswAAvV6PvXv3mjy2qKgIZWVlYg+VXq8Xe66MCgsLAaDeMo0aNUKTJpZl0DYGZsXFxRaVJyIiItvcKC1HZckNAFXfu+UNnKMFoEY2goZwaKAVFBSEoKCgestFR0dDq9Xi+PHj6NmzJwCgrKwMp0+fRsuWLQEAMTExWLBgAfLz8xEaWrUhblpaGrRaLaKjo8Uyzz//PEpLS+Hp6SmWCQsLQ6tWrcQyW7ZsMXn9tLQ0dOnSBR4eHha9L2NgyLlaRERE9hO6TJrnuXbtGnQ6nSTPpYpVhwCQlJSEzz77DO+//z5atmyJN954A1u2bMEvv/yCgIAAVFRUoGPHjggJCcEbb7yBK1euICEhAY888oiY3sFgMKBdu3bo06cPnn/+efz6669ISEjAyy+/bJLeISoqCuPHj0diYiIyMzMxYcIEfPzxxxand6isrMSFCxfg5+dX63CjLYyrGc+dO8fhSSuw3WzDdrMe28w2bDfbsN1sU1e7CYKAa9euISwsDG5uEs2uElSitLRUmDlzphAcHCz4+fkJ/fr1E3JyckzKnDlzRhg0aJDg7e0tBAYGCpMnTxZu3bplUubw4cPCgw8+KGi1WkGv1wtz584VKisrTcr88MMPQqdOnQRPT0+hVatWwsqVK2V/f5YwGAwCAMFgMDi6KqrCdrMN2816bDPbsN1sw3azjb3bTTU9WiRPfg9XwHazDdvNemwz27DdbMN2s429200V6R2IiIiI1IiBlopotVrMmTPHJOEq1Y/tZhu2m/XYZrZhu9mG7WYbe7cbhw6JiIiIZMIeLSIiIiKZMNAiIiIikgkDLSIiIiKZMNAiIiIikgkDLRX597//jYiICHh5eSE6Oho//fSTo6vkMOY2JNfr9eL9giBg7ty5CAsLg7e3N3r16oWjR4+aPEdJSQmmTJmCoKAg+Pr6YujQofj999/t/VZk8+OPP2LIkCEICwuDRqPBf//7X5P7pWqjoqIijBkzBjqdDjqdDmPGjMHVq1dlfnfyqa/dEhISapx73bt3Nynjau22aNEi3H///fDz80NwcDAeeeQRHD9+3KQMz7eaLGk3nm81rVy5Evfeey/8/f3h7++PmJgYfPvtt+L9ijvX7JIWlRps06ZNgoeHh7B69WohNzdXmDZtmuDr6yucOXPG0VVziDlz5gj33HOPkJ+fL94KCwvF+1977TXBz89P+Pzzz4UjR44Ijz/+uBAaGioUFxeLZSZMmCA0a9ZM2L59u3Dw4EGhd+/ewn333SeUl5c74i1J7ptvvhFeeOEF4fPPPxcACJs3bza5X6o2io+PF6KiooTdu3cLu3fvFqKiooTBgwfb621Krr52Gzt2rBAfH29y7l2+fNmkjKu1W1xcnLB27VohJydHyM7OFgYNGiS0aNFC+PPPP8UyPN9qsqTdeL7V9NVXXwlbt24Vjh8/Lhw/flx4/vnnBQ8PD3G3GKWdawy0VKJr167ChAkTTI7dfffdwnPPPeegGjnWnDlzhPvuu8/sfZWVlYJerxdee+018ditW7cEnU4nrFq1ShAEQbh69arg4eEhbNq0SSxz/vx5wc3NTUhNTZW17o5QPWCQqo1yc3MFAMKePXvEMpmZmQIA4ZdffpH5XcmvtkBr2LBhtT6G7SYIhYWFAgAhPT1dEASeb5aq3m6CwPPNUgEBAcJ7772nyHONQ4cqUFpaiqysLAwYMMDk+IABA7B7924H1crxfv31V4SFhSEiIgJPPPEETp06BaBqY/CCggKT9tJqtYiNjRXbKysrC2VlZSZlwsLCEBUV5RJtKlUbZWZmQqfToVu3bmKZ7t27Q6fTOXU7/vDDDwgODsZdd92FxMREFBYWivex3QCDwQAACAwMBMDzzVLV282I51vtKioqsGnTJly/fh0xMTGKPNcYaKnApUuXUFFRgZCQEJPjISEhKCgocFCtHKtbt2744IMPsG3bNqxevRoFBQXo0aMHLl++LLZJXe1VUFAAT09PBAQE1FrGmUnVRgUFBQgODq7x/MHBwU7bjg8//DA2btyIHTt2YMmSJdi/fz/69OmDkpISAGw3QRAwY8YM9OzZE1FRUQB4vlnCXLsBPN9qc+TIETRu3BharRYTJkzA5s2bERkZqchzrZFVpcmhNBqNyd+CINQ45ioefvhh8d8dOnRATEwM2rRpg/Xr14sTRW1pL1drUynayFx5Z27Hxx9/XPx3VFQUunTpgpYtW2Lr1q0YPnx4rY9zlXabPHkyDh8+jIyMjBr38XyrXW3txvPNvHbt2iE7OxtXr17F559/jrFjxyI9PV28X0nnGnu0VCAoKAju7u41oujCwsIaUbur8vX1RYcOHfDrr7+Kqw/rai+9Xo/S0lIUFRXVWsaZSdVGer0eFy9erPH8f/zxh0u0IwCEhoaiZcuW+PXXXwG4drtNmTIFX331FXbu3InmzZuLx3m+1a22djOH51sVT09P3HnnnejSpQsWLVqE++67D//6178Uea4x0FIBT09PREdHY/v27SbHt2/fjh49ejioVspSUlKCY8eOITQ0FBEREdDr9SbtVVpaivT0dLG9oqOj4eHhYVImPz8fOTk5LtGmUrVRTEwMDAYD9u3bJ5bZu3cvDAaDS7QjAFy+fBnnzp1DaGgoANdsN0EQMHnyZHzxxRfYsWMHIiIiTO7n+WZefe1mDs838wRBQElJiTLPNaumzpPDGNM7rFmzRsjNzRWSkpIEX19f4fTp046umkPMnDlT+OGHH4RTp04Je/bsEQYPHiz4+fmJ7fHaa68JOp1O+OKLL4QjR44II0aMMLu8t3nz5sJ3330nHDx4UOjTp49TpXe4du2acOjQIeHQoUMCACElJUU4dOiQmBJEqjaKj48X7r33XiEzM1PIzMwUOnTooNpl44JQd7tdu3ZNmDlzprB7924hLy9P2LlzpxATEyM0a9bMpdtt4sSJgk6nE3744QeTNAQ3btwQy/B8q6m+duP5Zl5ycrLw448/Cnl5ecLhw4eF559/XnBzcxPS0tIEQVDeucZAS0XefvttoWXLloKnp6fQuXNnkyXArsaYF8XDw0MICwsThg8fLhw9elS8v7KyUpgzZ46g1+sFrVYrPPTQQ8KRI0dMnuPmzZvC5MmThcDAQMHb21sYPHiwcPbsWXu/Fdns3LlTAFDjNnbsWEEQpGujy5cvC6NGjRL8/PwEPz8/YdSoUUJRUZGd3qX06mq3GzduCAMGDBCaNm0qeHh4CC1atBDGjh1bo01crd3MtRcAYe3atWIZnm811dduPN/Me+qpp8TvwqZNmwp9+/YVgyxBUN65phEEQbCuD4yIiIiILME5WkREREQyYaBFREREJBMGWkREREQyYaBFREREJBMGWkREREQyYaBFREREJBMGWkREREQyYaBFREREJBMGWkREVtJoNPjvf/8ry3OfPn0aGo0G2dnZsjw/EdkXAy0iUpzCwkKMHz8eLVq0gFarhV6vR1xcHDIzMx1dNdmFh4cjPz8fUVFRjq4KEUmgkaMrQERU3aOPPoqysjKsX78erVu3xsWLF/H999/jypUrjq6a7Nzd3aHX6x1dDSKSCHu0iEhRrl69ioyMDCxevBi9e/dGy5Yt0bVrVyQnJ2PQoEFiuZSUFHTo0AG+vr4IDw/HpEmT8Oeff4r3r1u3DnfccQe+/vprtGvXDj4+Pvi///s/XL9+HevXr0erVq0QEBCAKVOmoKKiQnxcq1at8Morr2DkyJFo3LgxwsLCsHz58jrrfP78eTz++OMICAhAkyZNMGzYMJw+fbrW8kVFRRg1ahSaNm0Kb29vtG3bFmvXrgVQc+gwISEBGo2mxu2HH34AAJSWlmL27Nlo1qwZfH190a1bN/E+InI8BlpEpCiNGzdG48aN8d///hclJSW1lnNzc8Nbb72FnJwcrF+/Hjt27MDs2bNNyty4cQNvvfUWNm3ahNTUVPzwww8YPnw4vvnmG3zzzTf48MMP8e677+Kzzz4zedwbb7yBe++9FwcPHkRycjKmT5+O7du3m63HjRs30Lt3bzRu3Bg//vgjMjIy0LhxY8THx6O0tNTsY1566SXk5ubi22+/xbFjx7By5UoEBQWZLfuvf/0L+fn54m3atGkIDg7G3XffDQD4+9//jl27dmHTpk04fPgw/va3vyE+Ph6//vprrW1HRHYkEBEpzGeffSYEBAQIXl5eQo8ePYTk5GTh559/rvMxn3zyidCkSRPx77Vr1woAhN9++008Nn78eMHHx0e4du2aeCwuLk4YP368+HfLli2F+Ph4k+d+/PHHhYcfflj8G4CwefNmQRAEYc2aNUK7du2EyspK8f6SkhLB29tb2LZtm9m6DhkyRPj73/9u9r68vDwBgHDo0KEa933++eeCVqsVfvrpJ0EQBOG3334TNBqNcP78eZNyffv2FZKTk80+PxHZF3u0iEhxHn30UVy4cAFfffUV4uLi8MMPP6Bz585Yt26dWGbnzp3o378/mjVrBj8/Pzz55JO4fPkyrl+/Lpbx8fFBmzZtxL9DQkLQqlUrNG7c2ORYYWGhyevHxMTU+PvYsWNm65qVlYXffvsNfn5+Ym9cYGAgbt26hZMnT5p9zMSJE7Fp0yZ07NgRs2fPxu7du+ttk0OHDuHJJ5/E22+/jZ49ewIADh48CEEQcNddd4mv3bhxY6Snp9f62kRkX5wMT0SK5OXlhf79+6N///54+eWX8fTTT2POnDlISEjAmTNnMHDgQEyYMAGvvPIKAgMDkZGRgXHjxqGsrEx8Dg8PD5Pn1Gg0Zo9VVlbWWx+NRmP2eGVlJaKjo7Fx48Ya9zVt2tTsYx5++GGcOXMGW7duxXfffYe+ffvimWeewZtvvmm2fEFBAYYOHYpx48Zh3LhxJq/t7u6OrKwsuLu7mzzm9mCSiByHgRYRqUJkZKSYu+rAgQMoLy/HkiVL4OZW1TH/ySefSPZae/bsqfG3cU5UdZ07d8Z//vMfBAcHw9/f3+LXaNq0KRISEpCQkIAHH3wQ//znP80GWrdu3cKwYcNw9913IyUlxeS+Tp06oaKiAoWFhXjwwQctfm0ish8OHRKRoly+fBl9+vTBhg0bcPjwYeTl5eHTTz/F66+/jmHDhgEA2rRpg/LycixfvhynTp3Chx9+iFWrVklWh127duH111/HiRMn8Pbbb+PTTz/FtGnTzJYdNWoUgoKCMGzYMPz000/Iy8tDeno6pk2bht9//93sY15++WV8+eWX+O2333D06FF8/fXXaN++vdmy48ePx7lz5/DWW2/hjz/+QEFBAQoKClBaWoq77roLo0aNwpNPPokvvvgCeXl52L9/PxYvXoxvvvlGsvYgItsx0CIiRWncuDG6deuGpUuX4qGHHkJUVBReeuklJCYmYsWKFQCAjh07IiUlBYsXL0ZUVBQ2btyIRYsWSVaHmTNnIisrC506dcIrr7yCJUuWIC4uzmxZHx8f/Pjjj2jRogWGDx+O9u3b46mnnsLNmzdr7eHy9PREcnIy7r33Xjz00ENwd3fHpk2bzJZNT09Hfn4+IiMjERoaKt6M87rWrl2LJ598EjNnzkS7du0wdOhQ7N27F+Hh4dI0BhE1iEYQBMHRlSAiUopWrVohKSkJSUlJjq4KETkB9mgRERERyYSBFhEREZFMOHRIREREJBP2aBERERHJhIEWERERkUwYaBERERHJhIEWERERkUwYaBERERHJhIEWERERkUwYaBERERHJhIEWERERkUz+P75yvWZvwlTlAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "parameter = houses['SalePrice'].mean()\n",
    "sample_size = 5\n",
    "\n",
    "sample_sizes = []\n",
    "sampling_errors = []\n",
    "\n",
    "for i in range(101):\n",
    "    sample = houses['SalePrice'].sample(sample_size , random_state = i)\n",
    "    statistic = sample.mean()\n",
    "    sampling_error = parameter - statistic\n",
    "    sampling_errors.append(sampling_error)\n",
    "    sample_sizes.append(sample_size)\n",
    "    sample_size += 29\n",
    "    \n",
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(sample_sizes, sampling_errors)\n",
    "plt.axhline(0)\n",
    "plt.axvline(2930)\n",
    "plt.xlabel('Sample size')\n",
    "plt.ylabel('Sampling error')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As seen above, the general tendency for the sampling error is to decrease as the sample size increases. This tendency, however, has exceptions. For instance, there are cases where small sample sizes (100-500 sample points) gave us better estimates for the population mean μ than large sample sizes (2500 sample points or more) did.\n",
    "\n",
    "![Smaller samples better](img/s2m1_smaller_samples_better.svg)\n",
    "\n",
    "For any given sample size, we can have many combinations of values. For instance, for a sample size of 3, we can have many possible combinations of sale prices: [220000, 143000, 281000], [123600, 209500, 202665], [287000, 142500, 440000], etc. Most of the samples of size 3 will give a good estimate of the population mean μ\n",
    "\n",
    "To prove this point, in the code below we will:\n",
    "\n",
    "+ Measure the mean for 10000 samples of size 3.\n",
    "+ Use a histogram to visualize the distribution of the sample means.\n",
    "+ Draw a vertical line corresponding to the population mean μ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7f074a333730>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means = []\n",
    "for i in range(10000):\n",
    "    sample = houses['SalePrice'].sample(3, random_state=i)\n",
    "    means.append(sample.mean())\n",
    "\n",
    "plt.hist(means)\n",
    "plt.axvline(houses['SalePrice'].mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that most sample means cluster around the population mean. This means that when we take a sample of size 3 and compute ¯x, we have fairly good chances to get a good estimate for the population mean μ. This explains what we've seen in the scatter plot above, where we got good estimates from low-sized samples."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Instructions\n",
    "\n",
    "Take 10000 samples of sample size 100 from the population of sale prices and measure the mean of each sample. For each of the 10000 iterations of a for loop:\n",
    "\n",
    "+ Use `Series.sample()` to take a sample of size 100 from the SalePrice variable. The random_state parameter is 0 for the first iteration, 1 for the second iteration, 2 for the third iteration, and so on.\n",
    "+ Compute the mean of the sample.\n",
    "\n",
    "+ Use `plt.hist()` to generate a histogram to visualize the distribution of sample means.\n",
    "\n",
    " + Draw a vertical line for the population mean.\n",
    " + Label the x-axis \"Sample mean\".\n",
    " + Label the y-axis \"Frequency\".\n",
    " + Set the range of the x-axis to (0,500000). This is the same range as the histogram we built above has. Can you observe any obvious difference between the two histograms now that we've increased the sample size?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 500000.0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means = []\n",
    "\n",
    "for i in range(10000):\n",
    "    sample = houses['SalePrice'].sample(100, random_state=i)\n",
    "    means.append(sample.mean())\n",
    "    \n",
    "plt.hist(means)\n",
    "plt.axvline(houses['SalePrice'].mean())\n",
    "plt.xlabel('Sample mean')\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlim(0,500000)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generally, as we increase the sample size, there will be less and less variability around the population mean. If there's less variability, there are less chances to get a poor estimate for the population mean — the worst sample means we can get are fairly close to the population mean, which is good."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Larger sample sizes are best estimators of population mean"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Variability](img/s2m1_sampling_distros.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean as Unbiased Estimator\n",
    "\n",
    "For many possible sampling combinations the mean will be the same\n",
    "\n",
    "When a statistic is on average equal to the parameter it estimates, we call that statistic an unbiased estimator. In our case, the sample mean ¯x is an unbiased estimator for the population mean μ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "population = [3, 7, 2]\n",
    "samples = [[3, 7], [3, 2],\n",
    "           [7, 2], [7, 3],\n",
    "           [2, 3], [2, 7]\n",
    "          ]\n",
    "\n",
    "sample_means = []\n",
    "for sample in samples:\n",
    "    sample_means.append(sum(sample) / len(sample))\n",
    "    \n",
    "population_mean = sum(population) / len(population)\n",
    "mean_of_sample_means = sum(sample_means) / len(sample_means)\n",
    "\n",
    "unbiased = (population_mean == mean_of_sample_means)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weighted Mean\n",
    "\n",
    "The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding Median\n",
    "\n",
    "+ Find the median value of the TotRms AbvGrd column. [Total rooms above the ground]\n",
    "\n",
    "+ Sort the values in the column in ascending order.\n",
    "    \n",
    "    + Replace the '10 or more' value with the integer 10 using the `Series.replace()` method. We do this only for sorting purposes. To avoid modifying the data in the original data set, make a copy of the column using the `Series.copy()` method and save it to a distinct variable.\n",
    "    + Convert the column to the int type using the `Series.astype()` method.\n",
    "    + Sort the values in ascending order using the `Series.sort_values()` method.\n",
    "\n",
    "+  Depending on whether the distribution has an odd or even number of values, find the median and assign it to a variable named median.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6             844\n",
       "7             649\n",
       "5             586\n",
       "8             347\n",
       "4             203\n",
       "9             143\n",
       "10 or more    131\n",
       "3              26\n",
       "2               1\n",
       "Name: TotRms AbvGrd, dtype: int64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['TotRms AbvGrd'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "houses_new = houses.copy()\n",
    "houses_new['TotRms AbvGrd'] = houses_new['TotRms AbvGrd'].replace('10 or more', 10)\n",
    "houses_new['TotRms AbvGrd'] = houses_new['TotRms AbvGrd'].astype('int')\n",
    "houses_new['TotRms AbvGrd'].sort_values().iloc[1464:1466]\n",
    "median=6"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Median a resistant statistic\n",
    "\n",
    "+ The `Lot Area` and `SalePrice` variables have outliers. Confirm this information by visualizing the distributions using a box plot. Remember from the previous course that outliers will appear as dots on the graph.\n",
    "    + You can use the `Series.plot.box()` method.\n",
    "    \n",
    "+ Compute the median and the mean for each of the two variables.\n",
    "    + Because the variables are numerical, you can use the `Series.median()` method and the `Series.mean()` method.\n",
    "\n",
    "+  For each variable, compute the difference between the mean and the median. \n",
    "    + Assign the difference for the Lot Area column to a variable named lotarea_difference.\n",
    "    + Assign the difference for the SalePrice column to a variable named saleprice_difference.\n",
    "    + Inspect the differences. Do you find the differences large?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "houses['Lot Area'].plot.box()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "houses['SalePrice'].plot.box()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "a= houses['Lot Area'].median()\n",
    "b=houses['SalePrice'].median()\n",
    "c=houses['Lot Area'].mean()\n",
    "d=houses['SalePrice'].mean()\n",
    "lotarea_difference=c-a\n",
    "saleprice_difference=d-b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3680.7051194539254"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lotarea_difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20796.060068259394"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "saleprice_difference"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Median for Ordinal Scales\n",
    "\n",
    "Data points belonging to ordinal variables are often coded using numbers. Consider the frequency distribution of the Overall Cond variable, which rates the overall condition of a house:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1       7\n",
       "2      10\n",
       "3      50\n",
       "4     101\n",
       "5    1654\n",
       "6     533\n",
       "7     390\n",
       "8     144\n",
       "9      41\n",
       "Name: Overall Cond, dtype: int64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['Overall Cond'].value_counts().sort_index()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because words like \"fair\" or \"average\" are coded with numbers, it becomes mathematically possible to compute the mean. But whether or not it's theoretically sound to compute the mean for ordinal variables is contentious."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The numerical values of an ordinal variable are not subject to meaningful arithmetical operations. But computing the mean involves meaningful arithmetical operations, so it's not theoretically sound to use the mean for ordinal variables.\n",
    "\n",
    "Because the median doesn't involve arithmetical operations, it's considered a better alternative to the mean. This doesn't fully apply, however, to even-numbered distributions, where we need to take the mean of the middle two values to find the median."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the mean and the median of the Overall Cond variable.\n",
    "\n",
    "+ Assign the mean to a variable named mean.\n",
    "+ Assign the median to a variable named median.\n",
    "\n",
    "Plot a histogram to visualize the distribution of the Overall Cond variable. Between the mean and the median, which one do you think describes better the shape of the histogram?\n",
    "\n",
    "+ If you think it's the mean, assign the string 'mean' to a variable named more_representative, otherwise assign 'median'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = houses['Overall Cond'].mean()\n",
    "median =  houses['Overall Cond'].median()\n",
    "\n",
    "houses['Overall Cond'].plot.hist()\n",
    "\n",
    "more_representative = 'mean'"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although it can be argued that it's theoretically unsound to compute the mean for ordinal variables, in the last exercise we found the mean more informative and representative than the median. The truth is that in practice many people get past the theoretical hurdles and use the mean nonetheless because in many cases it's much richer in information than the median."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mode\n",
    "\n",
    "+ Th most frequent value in a distribution\n",
    "+ `Series.mode()`\n",
    "Start from this task\n",
    "\n",
    "1. Explore the Land Slope column to find its scale of measurement. Refer to the documentation to find the data dictionary of this column.\n",
    "\n",
    " + Assign your answer as a string to the variable scale_land. Depending on the scale of measurement, choose between these following strings: 'nominal', 'ordinal', 'interval', and 'ratio'.\n",
    "\n",
    "2. Explore the Roof Style variable and find its scale of measurement. Assign your answer as a string to a variable named scale_roof (choose between the four strings listed above).\n",
    "\n",
    "+ What measure of average would you choose for this column?\n",
    "\n",
    "3. Explore the Kitchen AbvGr variable and determine whether it's continuous or discrete. Assign your answer as a string to a variable named kitchen_variable — the string should be either 'continuous', or 'discrete'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     2930\n",
       "unique       3\n",
       "top        Gtl\n",
       "freq      2789\n",
       "Name: Land Slope, dtype: object"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['Land Slope'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Gtl', 'Mod', 'Sev'], dtype=object)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['Land Slope'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Gtl    2789\n",
       "Mod     125\n",
       "Sev      16\n",
       "Name: Land Slope, dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['Land Slope'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    Gtl\n",
       "Name: Land Slope, dtype: object"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['Land Slope'].mode()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A custom function for mode\n",
    "Write a function that takes in an array of values (including strings) and returns the mode of that array. Inside the function's definition:\n",
    "\n",
    "+ Initialize an empty dictionary.\n",
    "\n",
    "+ Loop through the values of the array that the function takes in. For each iteration of the loop:\n",
    "\n",
    "  + If the value is already a key in the dictionary we initialized before the loop, increment its dictionary value by 1.\n",
    "  + Else, define the value as a key in the dictionary, and set the initial dictionary value to 1.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mode(array):\n",
    "    counts = {}\n",
    "    \n",
    "    for value in array:\n",
    "        if value in counts:\n",
    "            counts[value] += 1\n",
    "        else:\n",
    "            counts[value] = 1\n",
    "    \n",
    "    return max(counts, key = counts.get)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count      2930\n",
       "unique        6\n",
       "top       Gable\n",
       "freq       2321\n",
       "Name: Roof Style, dtype: object"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scale_land = 'ordinal'\n",
    "\n",
    "houses['Roof Style'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Gable      2321\n",
       "Hip         551\n",
       "Gambrel      22\n",
       "Flat         20\n",
       "Mansard      11\n",
       "Shed          5\n",
       "Name: Roof Style, dtype: int64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['Roof Style'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "scale_roof = 'nominal'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    1\n",
       "2    1\n",
       "3    1\n",
       "4    1\n",
       "Name: Kitchen AbvGr, dtype: int64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "houses['Kitchen AbvGr'].head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Skewed Distributions\n",
    "\n",
    "When we plot a histogram or a kernel density plot to visualize the shape of a distribution, the mode will always be the peak of the distribution. In the code below, we plot a kernel density plot to visualize the shape of the SalePrice variable and:\n",
    "\n",
    "+ Set the limits of the x-axis using the xlim parameter — the lowest limit is the minimum value in the SalePrice variable, and the upper limit is the maximum value.\n",
    "+ Plot a vertical line to indicate the position of the mode (note that our estimate of 150000 from the last exercise is quite close to the peak of the distribution)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7f0749378d90>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SZKrI9xW1mfaRJEnmaoAJ/RlUiIio+2QNKr/97W+xZ88evP766zh9+jQ+/fRTrFy5EkuWLJGzLJ/mDZu9teXsU9l3tgpCsE+FiIi6RtagMn78eKxfvx6fffYZUlJS8Ic//AF/+tOfsHDhQjnL8mmtQUW+pcltjUkMg06tQnmdGXkVDXKXQ0REPkbWfVQA4NZbb8Wtt94qdxl+47zJsTQ5zugdIyoBWjVGJxhxIK8K+85Von9UsNwlERGRD5F9C31yL29ZmtyW89yf/WfZp0JERF3DoOJnvK1HBQAmJLOhloiIuodBxY8IIbyuRwUAxiVFQJKAcxUNKK1tkrscIiLyIQwqfqSm0Yp6i+OkYm8aUTEGajE0xgAA2H+W2+kTEVHnMaj4EedhhBHBOgRo1TJX096EZOe5P5z+ISKizmNQ8SPeOO3j1HpAIYMKERF1HoOKH3EFFS9ZmtyWM6icLK5BbVOzzNUQEZGvYFDxI0XVjkZVb+pPcYo1BiAxIhB2AWTmsU+FiIg6h0HFjxSbvHfqB+D0DxERdR2Dih/xxj1U2prg2viNIypERNQ5DCp+5LwXT/0AwPiWlT+HC6thttpkroaIiHwBg4qfsNrsKKlxBBVv2j6/rQFRwYgM1sFitSOr0CR3OURE5AMYVPxEaa0ZNruARiUhKkQvdzkdkiQJaf0d2+nvY58KERF1AoOKn3A20sYaA6BWSTJXc3njeUAhERF1AYOKn/DmpcltOXeoPZBXBZtdyFwNERF5OwYVP+Fc8eOt/SlOI+JCEaxTo7bJiuySWrnLISIiL8eg4ie8efv8tjRqFcYmOfpUuJ8KERFdDYOKn3AuTY7zwu3zL8aN34iIqLMYVPyEr0z9AO2DihDsUyEiostjUPET503evSttW9ckhkGrlnChxoyCyka5yyEiIi/GoOIH6s1WVDc4TiT29h4VAAjUqZHS1wiA+6kQEdGVMaj4AeceKga9BoYArczVdM4E7qdCRESdwKDiB7z9jJ+OsKGWiIg6g0HFD/jK0uS2nFvp55bXo7zOLHM1RETkrRhU/EBrUPGdEZWwIB2GxhgAAAc4qkJERJfBoOIHfGX7/Iu5Dig8WyVzJURE5K0YVPxAscn3pn6A1nN/2KdCRESXw6DiB1xTPz6wK21bzoba4+dNqDNbZa6GiIi8EYOKj7PbBc6bfHPqJz4sEH3DAmEXwME8Tv8QEdGlGFR8XEW9BRarHZIExBp9a+oHaJ3+YUMtERF1hEHFxzmnfaINemjVvvef0zn9wx1qiYioI773k43aKfahM346Mr5l5c+h/GpYrHaZqyEiIm/DoOLjfHVpstOg6BCEB2lhttqRVWSSuxwiIvIysgaVl156CZIktXvExsbKWZLPcU799PXRoCJJEtK4nT4REV2G7CMqI0eORHFxseuRlZUld0k+xRlU4nywkdaJBxQSEdHlaGQvQKPhKEoP+OrS5LbGO1f+5FXBbhdQqSSZKyIiIm8h+4hKTk4O4uPjkZycjHvuuQe5ublyl+RTfH3qBwBGxociUKuGqbEZOaV1cpdDREReRNagMnHiRKxevRobN27EqlWrUFJSgilTpqCioqLD681mM2pqato9lMxstaGs1nHysC+PqGjVKoxNCgPAZcpERNSerEFlzpw5uPPOOzFq1CjMmjULX3/9NQDg448/7vD69PR0GI1G1yMxMbE3y/U6JS3TPnqNCuFBWpmr6Zm0JPapEBHRpWSf+mkrODgYo0aNQk5OToevL1++HCaTyfUoKCjo5Qq9S5Fz2ic8EJLk230dbQ8oFELIXA0REXkLrwoqZrMZJ0+eRFxcXIev6/V6hIaGtnso2fmWPVR8uT/FKbVfGDQqCcWmJhRWNcpdDhEReQlZg8ozzzyDHTt24OzZs9i7dy/uuusu1NTUYNGiRXKW5TN89dTkjgTpNBjZ1wiA+6kQEVErWYNKYWEh7r33XgwdOhTz58+HTqfDnj17kJSUJGdZPsMVVPxgRAUAJrRsp7//HE9SJiIiB1n3UVm7dq2cb+/zilxBxXc3e2trfP8IrPrhLEdUiIjIxat6VKhr/GEPlbacW+mfLq1DZb1F5mqIiMgbMKj4KCGEq5nWX6Z+IoJ1GBQdAoB9KkRE5MCg4qOqG5rR2GwDAMT68Dk/FxvPc3+IiKgNBhUf5exPiQrRI0Crlrka9xnf0lB7II8NtURExKDis1r7U/xnNAVo3aH2+HkTmlpGjIiISLkYVHyUvy1NdkqMCERUiB7NNoGjhSa5yyEiIpkxqPioIj8NKpIkIS3JMf2TyekfIiLFY1DxUf60ff7F0vo7gwobaomIlI5BxUf564gKAIxtM6LCAwqJiJSNQcVH+dtmb22lxBuh16hQ1dCM3PJ6ucshIiIZMaj4ILPVhtJaMwD/2T6/LZ1GhTEJYQCATJ77Q0SkaAwqPuiCyRFS9BoVIoJ1MlfjGWPZUEtERGBQ8UlFbaZ9JEmSuRrPcK78OcCGWiIiRWNQ8UH+uodKW84RlTNl9ajiAYVERIrFoOKDWoOK//WnOEUE6zCgTzAA4GA+p3+IiJSKQcUHnTf5/4gK0Hb6h0GFiEipGFR8UFHLZm/+HlTGsaGWiEjxGFR8kD/vodLWuJYDCo8UVMNitctcDRERyYFBxccIIRTRTAsAA6KCERakhdlqx/HzPKCQiEiJGFR8jKmxGQ0WGwAgzui/zbQAoFJJGNeP0z9ERErGoOJjnHuoRIXoEaBVy1yN543rz6BCRKRkDCo+pvXUZP8eTXFyjqgc4AGFRESKxKDiY4qqGgD4f3+K05jEMGhUEspqzSisapS7HCIi6mUMKj7mvEkZS5OdArRqjOxrBMDt9ImIlIhBxccUKWTFT1tp3E+FiEixuhVUzp496+46qJNa91BRRo8K0GaH2nMMKkREStOtoDJo0CDMmDEDa9asQVNTk7troitQyh4qbTl3qM2+UIvapmaZqyEiot7UraBy5MgRpKam4umnn0ZsbCweeeQR7Nu3z9210UUsVjtKa80AlBVUokMDkBgRCCGAQ/nVcpdDRES9qFtBJSUlBe+88w6KioqQkZGBkpISXHvttRg5ciTeeecdlJWVubtOAlBsaoQQgF6jQmSwTu5yelXbZcpERKQcPWqm1Wg0+MUvfoG///3vePPNN3HmzBk888wzSEhIwAMPPIDi4mJ31UmAa3luQnggJEmSuZreNa6/49yfgwwqRESK0qOgcuDAAfzmN79BXFwc3nnnHTzzzDM4c+YMtm7diqKiItx+++3uqpMAFFQ69lBJjAiSuZLe52yoPZRfBauNBxQSESmFpjtf9M477yAjIwPZ2dm45ZZbsHr1atxyyy1QqRy5Jzk5GR988AGGDRvm1mKVrqBls7fEcOUFlSExBhj0GtSarci+UIuR8Ua5SyIiol7QrRGVFStW4Je//CXy8/OxYcMG3Hrrra6Q4tSvXz98+OGHbimSHNpO/SiNWiXhmn5hALifChGRknQrqGzevBnPPvssYmNj2z0vhEB+fj4AQKfTYdGiRT2vkFyUPPUDAGlJjj6VvWe5Qy0RkVJ0K6gMHDgQ5eXllzxfWVmJ5OTkbhWSnp4OSZLw1FNPdevrlUDJIyoAMGlAS1DJreQBhURECtGtoHK5HxJ1dXUICOj6jqn79+/HypUrMXr06O6UowhNzTbXHipK7FEBHAcU6jUqlNeZcaasXu5yiIioF3SpmXbZsmUAAEmS8MILLyAoqPUHps1mw969e3HNNdd0qYC6ujosXLgQq1atwquvvtqlr1US52hKiF6DsCCtzNXII0Crxth+4didW4E9uRUYFB0id0lERORhXQoqhw4dAuAYUcnKyoJO17rpmE6nw5gxY/DMM890qYAlS5Zg7ty5mDVr1lWDitlshtlsdn1eU1PTpffyZYUtK36UuIdKW5MGRLqCyn2TkuQuh4iIPKxLQWXbtm0AgAcffBDvvvsuQkNDe/Tma9euxcGDB7F///5OXZ+eno6XX365R+/pqwpc/SnKnPZxcvap7GnpU1FyaCMiUoJu9ahkZGT0OKQUFBTgySefxJo1azrd17J8+XKYTCbXo6CgoEc1+JK2IypKxj4VIiJl6fSIyvz58/HRRx8hNDQU8+fPv+K169atu+r3y8zMRGlpKcaNG+d6zmazYefOnXjvvfdgNpuhVqvbfY1er4der+9syX6lsNIxoqLUpclO7FMhIlKWTgcVo9HoGmY3Gnu+K+jMmTORlZXV7rkHH3wQw4YNw7PPPntJSFG6Ao6ouLBPhYhIOTodVDIyMjr8uLsMBgNSUlLaPRccHIzIyMhLnqfWVT9KXZrcFvtUiIiUo1s9Ko2NjWhoaHB9npeXhz/96U/YtGmT2wqjVvVmKyrrLQCAhAiOqLBPhYhIObp1KOHtt9+O+fPn49FHH0V1dTUmTJgAnU6H8vJyvPPOO3jssce6Vcz27du79XX+zjmaYgzUIjRAmXuotMU+FSIi5ejWiMrBgwcxbdo0AMA///lPxMbGIi8vD6tXr8af//xntxZIbc/44WiK06QBkQCAn05fepQDERH5j24FlYaGBhgMBgDApk2bMH/+fKhUKkyaNAl5eXluLZDaNNKGsT/FadqQKACOoGK12WWuhoiIPKVbQWXQoEHYsGEDCgoKsHHjRsyePRsAUFpa2uP9VehSrkZajqi4jEkIgzFQi5omK44UmuQuh4iIPKRbQeWFF17AM888g/79+2PixImYPHkyAMfoSmpqqlsLpNapH6XvStuWWiXh2kGOUZUfcspkroaIiDylW0HlrrvuQn5+Pg4cOIDvvvvO9fzMmTPx3//9324rjhwKOKLSoWmDHUFl5ykGFSIif9WtVT8AEBsbi9jY2HbPTZgwoccF0aWc2+dzD5X2pg3pAwA4XFANU0MzjAo9VZqIyJ91K6jU19fjjTfewPfff4/S0lLY7e2bGXNzc91SHAGmhmbUNlkBAH25K207fcMCMbBPMM6U1WPXmXLMGRUnd0lERORm3QoqDz/8MHbs2IH7778fcXFx3BnUg85VODY0izboEaTr9gCY37puSB+cKavHzpwyBhUiIj/UrZ983377Lb7++mtMnTrV3fXQRZxBpX9ksMyVeKfrhvRBxk/nsPNUObfTJyLyQ91qpg0PD0dERIS7a6EO5FU4+lOSItmf0pGJyRHQqVUoqm5Ebjm30yci8jfdCip/+MMf8MILL7Q774c8wzWiEsURlY4E6TQYnxwOgKt/iIj8Ubemft5++22cOXMGMTEx6N+/P7Ta9qstDh486JbiiCMqnXH9kGj8dLoC358sxYNTk+Uuh4iI3KhbQeWOO+5wcxl0Oa6gEsERlcuZNSIGr31zEntyK2BqbIYxkMuUiYj8RbeCyosvvujuOqgDdWYryuvMAIB+HFG5rOSoYAyKDsHp0jpszy7F7df0lbskIiJyk271qABAdXU1/va3v2H58uWorKwE4JjyKSoqcltxSpfX0p8SEazjKMFV3DgiBgCw+cQFmSshIiJ36lZQOXr0KIYMGYI333wTb731FqqrqwEA69evx/Lly91Zn6KxP6XznEFlR3YZLFaepkxE5C+6FVSWLVuGxYsXIycnBwEBAa7n58yZg507d7qtOKXjHiqdd01CGPoY9Kg1W7Ent0LucoiIyE26FVT279+PRx555JLn+/bti5KSkh4XRQ555RxR6SyVSsKs4dEAOP1DRORPuhVUAgICUFNTc8nz2dnZ6NOnT4+LIgeOqHSNc/pny8kLEELIXA0REblDt4LK7bffjldeeQXNzc0AAEmSkJ+fj+eeew533nmnWwtUMvaodM2UgVEI0qlRbGrCsaJLgzQREfmebgWVt956C2VlZYiOjkZjYyOmT5+OQYMGwWAw4LXXXnN3jYrU1GxDSU0TACCJIyqdEqBV47rBjhG9744Xy1wNERG5Q7f2UQkNDcWPP/6Ibdu2ITMzE3a7HWPHjsWsWbPcXZ9i5Vc6RlMMARqEB3FpcmfdMjoO3x0vwb+PFuOZ2UN5SCERkY/rclCx2+346KOPsG7dOpw7dw6SJCE5ORmxsbE8vdaNzpW39qfwnnberOHRCNSqkVfRgKwiE0YnhMldEhER9UCXpn6EELjtttvw8MMPo6ioCKNGjcLIkSORl5eHxYsX4xe/+IWn6lQc9qd0T5BOg5ktq3++OnJe5mqIiKinuhRUPvroI+zcuRPff/89Dh06hM8++wxr167FkSNHsGXLFmzduhWrV6/2VK2KwhU/3TdvTDwA4N9Hi2G3c/UPEZEv61JQ+eyzz/D8889jxowZl7x2ww034LnnnsMnn3zituKUjCMq3Td9SB8Y9BoUm5pwIK9K7nKIiKgHuhRUjh49iptvvvmyr8+ZMwdHjhzpcVHUZkQliiMqXRWgVeOmlFgAnP4hIvJ1XQoqlZWViImJuezrMTExqKri/8H2lNlqw/nqRgBAUgRHVLrDOf3zTVYxrDae/UNE5Ku6FFRsNhs0mssvFFKr1bBarT0uSunyKxpgF0CwTo0+Br3c5fikKQMjERGsQ0W9BT+d4dk/RES+qkvLk4UQWLx4MfT6jn94ms1mtxSldGfKHNM+A6NDuDS5m7RqFW4ZFYs1e/Kx/mAhpg/h0Q5ERL6oS0Fl0aJFV73mgQce6HYx5HCmrA4AMID9KT1y59gErNmTj2+PleCVpmaEBnDjPCIiX9OloJKRkeGpOqiN3JYRlQF9QmSuxLddkxiGQdEhOF1ah38fKcYvJ/aTuyQiIuqibp31Q56VW+4YURnIoNIjkiRhwbgEAMA/MgtkroaIiLqDQcXLCCFwprRl6qcPp3566hdj+0KtknAovxqnS2vlLoeIiLpI1qCyYsUKjB49GqGhoQgNDcXkyZPx7bffylmS7CrqLahpskKSgGT2qPRYtCEA17c00v4js1DmaoiIqKtkDSoJCQl44403cODAARw4cAA33HADbr/9dhw/flzOsmTl7E+JNwYiQKuWuRr/sCDNMf2z7mAR91QhIvIxsgaVefPm4ZZbbsGQIUMwZMgQvPbaawgJCcGePXvkLEtWuS0rfgZGsz/FXW4YFoOIYB3Kas3YcapM7nKIiKgLvKZHxWazYe3ataivr8fkyZM7vMZsNqOmpqbdw99wabL76TQq3HFNXwDAZ/vyZa6GiIi6QvagkpWVhZCQEOj1ejz66KNYv349RowY0eG16enpMBqNrkdiYmIvV+t5zqmfgWykdSvn0uStP5eiqOV4AiIi8n6yB5WhQ4fi8OHD2LNnDx577DEsWrQIJ06c6PDa5cuXw2QyuR4FBf635DS33BlUOPXjToOiQzB5QCTsAljLURUiIp8he1DR6XQYNGgQ0tLSkJ6ejjFjxuDdd9/t8Fq9Xu9aIeR8+BOL1Y78ygYA3OzNExZOcoyqrN1fgGY21RIR+QTZg8rFhBCKPTMot7wONruAQa9BTCgPI3S32SNiERWiR1mtGZtPXJC7HCIi6gRZg8rzzz+PH374AefOnUNWVhZ+97vfYfv27Vi4cKGcZcnm1AVHI+3gGB5G6Ak6jQp3j3csVV6zJ0/maoiIqDNkDSoXLlzA/fffj6FDh2LmzJnYu3cvvvvuO9x4441yliWbnAuOnVOHxBhkrsR/3TuhHyQJ2HWmwrXCioiIvFeXDiV0tw8//FDOt/c6p1qCymAGFY9JCA/CjKHR2PpzKf53dx5eum2k3CUREdEVeF2PipLltEz9DIlhI60nLZ7SHwDwz8xC1DY1y1sMERFdEYOKl2hqtuFchWNpMqd+PGva4CgMig5BndmKvx/g+T9ERN6MQcVL5JbVwy6A0AANog1c8eNJkiThwan9AQAf7ToLm13IWxAREV0Wg4qXyCltbaTlih/Pm5+aAGOgFgWVjfj+JJcqExF5KwYVL8FG2t4VqFPj3gmODeD+56ezMldDRESXw6DiJU6xkbbXPTA5CWqVhD25lThx3v8OuCQi8gcMKl6Ce6j0vviwQMxJiQUAZHBUhYjIKzGoeIGmZhvyWs74GcwRlV714NRkAMC/jpxHeZ0yj24gIvJmDCpe4HRpHYQAwoK06BPCFT+9aWy/MIxJDIPFasf/7ua2+kRE3oZBxQu4VvxEc8VPb5MkCb+a5hhV+Xj3OTRYrDJXREREbTGoeIG2hxFS75uTEoekyCBUNzTj8/0FcpdDRERtMKh4ATbSykutkvDr6wYAAP72w1k02+wyV0RERE4MKl6AIyryu3NsAqJC9CiqbsRXR87LXQ4REbVgUJFZvdmKgirHih+OqMgnQKt2bav/wY5cCMFt9YmIvAGDisx+LqmFEEC0QY8orviR1X2TkhCi1yD7Qi22ZZfKXQ4REYFBRXYnih07og6PC5W5EjIGavHLiY5t9f+6PVfmaoiICGBQkZ1z6/YR8Qwq3uChqcnQqiXsO1eJzLxKucshIlI8BhWZnWwZURnBERWvEGsMwPzUBADAn78/LXM1RETEoCIjm13g5xKOqHibJTMGQa2SsONUGQ7lV8ldDhGRojGoyOhseT2amu0I1KrRPzJY7nKoRb/IINw5ti8A4N3vc2SuhohI2RhUZOSc9hkaa4Baxa3zvcnSGYOhVknYns1RFSIiOTGoyMi54ofTPt6nX2QQ5qdyVIWISG4MKjJyrfhhI61XWnrDINeoyuGCarnLISJSJAYVGXFExbslRQbjF85RlS2nZK6GiEiZGFRkUlZrRlmtGZIEDIvl1vneamnLCqBtHFUhIpIFg4pMnI20yZHBCNJpZK6GLqd/VOuoypvf/swzgIiIehmDikxcW+dz2sfrPTVrMHRqFXbnVmBnTrnc5RARKQqDikzYSOs7EsKD8MDkJACOURW7naMqRES9hUFFJifZSOtTlswYBINegxPFNfjq6Hm5yyEiUgwGFRk0WKw4U1YHABjJERWfEB6swyPTBwAA3t50CharXeaKiIiUgUFFBsfP18AugJhQPaJDA+QuhzrpoWuT0cegR35lAz7bly93OUREisCgIoOjhSYAwOiEMHkLoS4J0mnw5MzBAIA/f5+DOrNV5oqIiPwfg4oMjhZWAwBG9zXKWwh12d3jE5EcFYyKegtWbD8tdzlERH5P1qCSnp6O8ePHw2AwIDo6GnfccQeys7PlLKlXuEZUEsPkLYS6TKtWYfmcYQCAVT+cRUFlg8wVERH5N1mDyo4dO7BkyRLs2bMHmzdvhtVqxezZs1FfXy9nWR5lamzG2XLH748jKr7pxhExmDooEharHa9/c1LucoiI/JqsW6J+99137T7PyMhAdHQ0MjMzcd1118lUlWcdK3KMpiRGBCI8WCdzNdQdkiThhVtHYs67O/HtsRLsOlOOKQOj5C6LiMgveVWPisnk+CEeERHR4etmsxk1NTXtHr7miLM/hY20Pm1orAELJzo2gXvlqxOwcRM4IiKP8JqgIoTAsmXLcO211yIlJaXDa9LT02E0Gl2PxMTEXq6y544WOMLYmARO+/i6ZTcOgTFQi59LarF2P5crExF5gtcElaVLl+Lo0aP47LPPLnvN8uXLYTKZXI+CgoJerNA9jnJExW+EB+vw21mO5cpvbcyGqaFZ5oqIiPyPVwSVxx9/HF9++SW2bduGhISEy16n1+sRGhra7uFLymrNOG9qgiQBKWyk9QsLJyVhcHQIqhqa8dYm/1+xRkTU22QNKkIILF26FOvWrcPWrVuRnJwsZzkel1VUDQAY2CcEIXpZ+5jJTbRqFV6+bSQAYM3ePBwpqJa3ICIiPyNrUFmyZAnWrFmDTz/9FAaDASUlJSgpKUFjY6OcZXnMkQLnjrQcTfEnUwZF4Y5r4iEE8PsNx9hYS0TkRrIGlRUrVsBkMuH6669HXFyc6/H555/LWZbHOPtTxrA/xe/8bu4IGAI0yCoy4ZO9eXKXQ0TkN2Sf+unosXjxYjnL8gghhGtH2lEcUfE7fQx6/NdNQwEAf/wuG6W1TTJXRETkH7yimVYJ8isbUFFvgU6twog432oCps755cQkjE4wotZsxWtfc8daIiJ3YFDpJZl5VQCAlL6hCNCqZa6GPEGtkvDqHSmQJOBfh8/jh5wyuUsiIvJ5DCq9xBlUxiWFy1wJedLohDAsmtwfALB8XRYaLFZ5CyIi8nEMKr2EQUU5nrlpKOKNASisasTbm07JXQ4RkU9jUOkFtU3NyL5QCwAY249Bxd+F6DV4bf4oAEDGT2dxmHurEBF1G4NKLzhcUA0hHCcmR4cGyF0O9YIZQ6NxxzXxsAvg2X8ehcVql7skIiKfxKDSC5zTPmlJHZ8KTf7phXkjERGsQ/aFWvx1xxm5yyEi8kkMKr3AGVTGsj9FUSKCdXhx3ggAwHtbT+N0aa3MFRER+R4GFQ+z2QUO51cDAMaxP0VxbhsTjxuGRcNis+O//nmU2+sTEXURg4qH5ZTWotZsRbBOjaGxBrnLoV4mSY69VUL0GhzMr0bGT2flLomIyKcwqHiYc9ontV841CpJ5mpIDvFhgXj+luEAgD9uzMbp0jqZKyIi8h0MKh7G/hQCgHsnJOK6IX1gttrx9D+OwGrjKiAios5gUPEwbvRGgGMK6M07R8EQoMGRgmp8sDNX7pKIiHwCg4oHlZiakFfRAJUEpPYLk7scklmcMRAvzRsJAPjTllM4WVwjc0VERN6PQcWD9uRWAABG9TUiNEArczXkDeaP7YsbR8Sg2Sbw9N+PcCM4IqKrYFDxoN1nHEFl0oBImSshbyFJEl7/xSiEB2lxorgG723NkbskIiKvxqDiQXvOtgSVgQwq1KqPQY9X73CcBfT/tp/B0cJqeQsiIvJiDCoecr66EXkVDVCrJKSxkZYuMnd0HG4dHQebXWDZ34+gqdkmd0lERF6JQcVDnP0pKX2NMLA/hTrwh9tT0Megx+nSOrzx7c9yl0NE5JUYVDzE2Z8ymf0pdBnhwTr88a7RAICPdp3D1p8vyFwREZH3YVDxEFd/ygCemEyXd/3QaDw0NRkA8H/+cRSltU0yV0RE5F0YVDygsKoBBZWNUKskjO/PoEJX9l83D8WwWAMq6i34P/84CjsPLiQicmFQ8YA9uZUAgNEJRgTrNTJXQ94uQKvGX+5NhV6jwo5TZcjYdU7ukoiIvAaDigewP4W6anCMAb+/dQQA4M1vf0ZWoUnmioiIvAODipsJIVwrfrjRG3XFfRP7YfaIGFhsdjz2SSaqGyxyl0REJDsGFTc7U1aPoupG6DQq9qdQl0iShD8uGIN+EUEorGrE038/wn4VIlI8BhU323mqDAAwoX8EAnVqmashX2MM1OL9hWOh06jw/c+lWLHjjNwlERHJikHFzXbmOILKdUOiZK6EfFVKXyP+cLvjlOW3N2Vj28+lMldERCQfBhU3amq2ufpTrhvSR+ZqyJf9R1oi7hmfCLsAHv/sEH4uqZG7JCIiWTCouNGBc1VoarYjJlSPoTEGucshHyZJEl65PQWTB0SizmzFf350AGW1ZrnLIiLqdQwqbrTjlGOIftrgPpAkSeZqyNfpNCqsuG8skqOCUVTdiF+tPoB6s1XusoiIehWDihvtPFUOAJjOaR9yk7AgHf5n8XgYA7U4XFCNhz8+wJOWiUhRGFTcpKCyAdkXaqFWSZg2mI205D7JUcH46MHxCNapsTu3Ar/+30yYrQwrRKQMDCpu8v1Jx8m3aUnhCAvSyVwN+ZvUfuHIeHACArVq7DxVht+sOciRFSJSBFmDys6dOzFv3jzEx8dDkiRs2LBBznJ6ZMtJR3/KrOExMldC/mpCcgQ+XJQGfcseKw/8zz6YGprlLouIyKNkDSr19fUYM2YM3nvvPTnL6LGapmbXsuRZIxhUyHOmDIrCRw9OgEGvwb6zlbjrr7twpqxO7rKIiDxG1qAyZ84cvPrqq5g/f76cZfTYzlNlsNoFBvYJRnJUsNzlkJ+bPDASf390MmJC9cgprcNtf/kRXx8tlrssIiKP8KkeFbPZjJqamnYPb7DlhKM/hdM+1FuGx4Xiq6XXYkJyBOotNiz59CBe+vI4Gi3sWyEi/+JTQSU9PR1Go9H1SExMlLskWKx2bG3Z4pzTPtSbokMD8OnDE/Ho9IEAgI92ncPN7+50TUMSEfkDnwoqy5cvh8lkcj0KCgrkLgk/nS5HTZMV0QY9xvYLl7scUhiNWoXn5gxDxoPjERsagLyKBtyzcg+eX58FUyMbbYnI9/lUUNHr9QgNDW33kNu/W3oD5qTEQq3ibrQkjxlDo7Fp2XX45cR+AIBP9+Zj5ts78K/DRRBCyFwdEVH3+VRQ8TZmqw2bTpQAAOaOjpe5GlK60AAtXv/FKKz99SQM7BOM8joznlx7GA/8zz6cK6+Xuzwiom6RNajU1dXh8OHDOHz4MADg7NmzOHz4MPLz8+Usq9N+Ol2O2pZpn7QkTvuQd5g0IBLfPDkNT984BDqNCj/klGP2n3biz9/ncEdbIvI5sgaVAwcOIDU1FampqQCAZcuWITU1FS+88IKcZXWac9rnllFxUHHah7yIXqPG4zMHY9NT12Ha4ChYrHa8s/kU5rz7A3adKZe7PCKiTtPI+ebXX3+9z86fN1ps2HTcsSx57ug4mash6lj/qGCsfmgCvjpajFe+OoHcsnr8ctVeLBiXgBdvG4kQvaz/BBARXRV7VLpp4/ES1JmtSIwIxDiu9iEvJkkSbhsTj++fno77JyVBkoB/ZBZi3l9+xLEik9zlERFdEYNKN31xsBAAcOfYBE77kE8wBmrxhztS8PmvJyPOGICz5fWY//4urN59zmdHNonI/zGodMP56kb8eNoxz3/n2ASZqyHqmgnJEfjmiWmYNTwGFpsdL/zrOJavy4LFape7NCKiSzCodMP6Q0UQwvEPfmJEkNzlEHVZeLAOqx4Yh+dvGQaVBKzdX4D7/rYXFXVmuUsjImqHQaWL7HaBf2Y6pn3uGsfRFPJdkiTh19cNxIeLxztOYz5Xidve+wkni73jDC0iIoBBpct+PF2Os+X1MOg1mDuKq33I980YGo31S6agf2QQiqobcdeKXdj68wW5yyIiAsCg0mWrd+cBAO4cl4BgLu0kPzEo2oANS6ZiysBI1FtsePjjA8j46azcZRERMah0RWFVg+v/NO+blCRzNUTuFRakw8cPTcDdaYmwC+Dlr07ghX8dg9XGJlsikg+DShd8sjcfdgFcOygKg6JD5C6HyO20ahXeuHMUls8ZBklyjCD+58cHUNvEk5iJSB4MKp1Ub7bis32OM4jun8zRFPJfkiThkekDsWLhWARoVdhxqgx3rdiNwqoGuUsjIgViUOmkT/fmo7qhGQOigjFreIzc5RB53M0pcfj7I5PRx6BH9oVa3PbeT9ieXSp3WUSkMAwqnWC22rDqh1wAwCPTB0DNnWhJIUYnhOFfS6ZiZHwoKustWJyxH3/c+DP7Voio1zCodMIXmUUorTUjzhiAX6Ry7xRSlviwQHzx2BTcN6kfAOD/bTuDu1fuwZmyOpkrIyIlYFC5CrPVhve3nwYAPDxtAHQa3jJSngCtGq/eMQp/vjcVIXoNMvOqMOfdH/Dn73PQaLHJXR4R+TH+1L2KT/bko7CqEdEGPX45oZ/c5RDJ6rYx8fjuqWmYPqQPLFY73tl8Cte/tQ1r9uShqZmBhYjcj0HlCmqamvGXrTkAgN/eOASBOrXMFRHJLyE8CB89OB5/uTcVCeGBuFBjxu83HMOUN7bi9W9O4liRiacxE5HbcGvVK/hgxxlUNTRjYJ9gLOC5PkQukiRh3ph4zB4Zg0/35uPDH8+isKoRK3fmYuXOXMQZAzB5QCRGJRgxKDoEg6JDEG0IYCM6EXUZg8pl5JbVYdVOxxbi/3XzMGjUHHwiupheo8aDU5Nx/6QkfP9zKf51uAjfnyxFsakJ6w4VYd2hIte1KgmICNYhMliPyBAdIkP0iArRISY0ANEGPWJCA9AvIgh9wwKhYqAhohYMKh0QQuD3G47BYrPjuiF9MHsE900huhKNWoWbRsbippGxaLTYkJlXhb1nK5BdUovTZXXIq2iAzS5QXmdBeZ0FuMKZh4FaNQZFh2BUghFpSeFIS4pAYkQgJInhhUiJGFQ6sP5QEXadqYBeo8Krt6fwH0iiLgjUqXHt4ChcOzjK9VyzzY6qekdIqay3oKLejLJaM8rqzCitMaO0tgklpibkVzagsdmGrCITsopM+HSvYzfoaIMe1w6KwvXDonHd4CiEBenk+u0RUS9jULnI+epGvPzVCQDAEzMHo19kkMwVEfk+rVqF6NAARIcGXPG6Zpsd+ZUNOFVSi4P5VTiQV4VjRSaU1ppdU0kqCRiXFI7rh0bjxhExGBwdwv+ZIPJjDCpt2OwCv/38MEyNzRidYMSvpg2QuyQiRdGqVRjYJwQD+4Rgzqg4AEBTsw0H86uwI7sM27JLcepCHfafq8L+c1X448ZsJEcFY/bIGNw0MhbXJISxv4XIz0jCh9cR1tTUwGg0wmQyITQ0tMff7y/f5+DtzacQpFPj6yemITkq2A1V+od6Sz1C0h0nRtctr0OwjveG5FFY1YDt2WX4/uQF/HS6ApY22/nHhOpx4whHaJk0IBJaNsETeaWu/PzmiEqLTcdL8M6WUwCAl28byZBC5KUSwoNw36Qk3DcpCbVNzdieXYaNx0uwPbsMF2rMWLMnH2v25CM0QIOZw2Nw08gYXDekD4J0/OeOyBfxby6AE+dr8NTnhyEEcN+kfriLe6YQ+QRDgBbzxsRj3ph4mK027DpdgY3HS7D5xAVU1Fuw/lAR1h8qQoBWhWmD++DmkbGYOTyazbhEPkTxUz9nyupwz8o9KKs149pBUch4cDyHizvAqR/yJTa7QGZeFTYeL8HG4yUorGp0vaZWSZg8IBI3pcRi9ogYxFylwZeI3K8rP78VHVTOldfj7pW7caHGjGGxBnz+68kwBmk9UKnvY1AhXyWEwIniGmw8VoKNxy8g+0Jtu9fH9gtz7QHTn1O+RL2CQaUTDhdU4+GP96O8zoIhMSH47FeTEBmi91Clvo9BhfzF2fJ610jLofzqdq8NizW4QsvwOAOXPRN5CIPKVfz76Hk8848jaGq2Y0RcKD5+aAL6GBhSroRBhfxRiakJm0+U4LvjJdiTWwmbvfWfw4hgHcb3D8fE5EhMSI7A4JgQ6DU8mJTIHRhULqPRYsMr/z6Oz/YVAABmDO2Dv/xyLEL07Cm+GgYV8ndV9RZ8/3MpNh4vwQ85ZWhqtrd7XaOSkBwVjCGxBgyJNqBveCDijAEtj0Cerk7UBVye3IHvT17AS18dR0FlIyQJeGz6QCy7cQgPGyQiAEB4sA53jUvAXeMSYLHakVVUjb1nK7HvbCUO5lWhpsmKnNI65JTW4WsUX/L1wTo1ogx6RIXo0SdEjyiDDlEhetejj0GHPiEBiDLouFSaqAv8/m/Lwfwq/PfmU/ghpxwAEGcMwFsLxmDqoKirfCURKZVOo8K4pAiMS4rAb653NOSW1DQhu6QW2SW1OFNWh2JTE85XN6LY1IQGiw31FhvqKxqQV9Fw1e8fpFO3BJiWMGNwhJvoUD36RQShX0QQ4sMCuQKRCH4aVMxWGzafuID/3Z2HvWcrATiGbf/z2mQ8MXMwgjnVQ0RdIEkS4oyBiDMG4vqh0e1eE0Kg1mxFea255XRos+NRa0ZZnQVltebW5+rMaGq2o8FiQ35lA/IrLx9q1CoJ8WEBruCSGBGEpIhg1+dcoUhKIftP7Pfffx9//OMfUVxcjJEjR+JPf/oTpk2b1uXvY2psxq7T5fjueAm2nixFrdkKwPGXfX5qXzx+Aw8YJCL3kyQJoQFahAZoMaDPla8VQqDeYmsJNY5HWUugKa8zo8TUhIKWAGO22lFQ2YiCykb8hIpLvldogAZJkcGuENMvIghJkY5f44wBnNYmvyFrUPn888/x1FNP4f3338fUqVPxwQcfYM6cOThx4gT69evX6e8z//2fcMZkR9u24JhQPe5OS8S9E/shzhjogeqJiLpGkiSE6DUI0WuuuGeL3S5QVmd2jLpUNLhGX5yPslozapqsyCoyIavIdMnXq1US+oYFIinSEWL6hgUiIliHiGAdIlt+NQZqEaBVI0CrhrrNQY5CCNgFYLXbYbHa0dhsg7nZ8WujxYamZhsamx2/NrV93mpDk8XxWmPLaxIAvVYFvUYNnUYFvcbxsV6jgl6rQoBG3f5XreO1AK0abc+WbPtvu2j53C4E7EK4PrbZHXU767/4dedzQgjY7Y6P9Vo1ArVqBGhVLb+qEahTIzRAC52GQc9byLrqZ+LEiRg7dixWrFjhem748OG44447kJ6eftWvd3YNJz71d6j0QRgQFYxZLQeSpSbyFFV34qofIu/RYLGisKoReS0hxjkKk1dRj4KqRlis9qt/kza0aglqlQSrTcBq99mFoG4VotfAGKhFeLAW4UE6hAXpEBaoRXiQFqGBWoQFOcKe8xEWpHWFP6Wx2wUsNjvMVjvMVhssVsfH7X+1QQhHG4ZKJaGpvhYzRid796ofi8WCzMxMPPfcc+2enz17Nnbt2tXh15jNZpjNZtfnNTU1AIB3/mMMrkvph2gDt8ImIv8XpNNgSIwBQ2IMl7xmtwuU1ppdwSW/sgEXappQUWdBRb0FlfUWVNSZUW+xub6m2SbQbLt8QAlsGWkI0KgQoHOMQjhHIJyjEIEtIyJtnxcQrh9W5mbHDytzy+dNzbZ2v5pbRmmcz11cTdv/7VRJEiRJgkpyfKxWSZBaPnY+J7V7rfV5lQTXRn6WlvdyjhI5R4IAoM5sRZ3ZiqLqRnSFTqNCaIAWgTrH6FHARSNHOo0KKpXkqkXd5vfStla1SnL9np33QghAtHzmHGJo+1rbZ4Roe82Vv8b5ut3u+HNgttrRbGt9WKx2WGyi3edtA8iV/uxcjt189aZzJ9mCSnl5OWw2G2JiYto9HxMTg5KSkg6/Jj09HS+//PIlz88eGYtQhhQiIqhUEmKNAYg1BmBCcsRlr7PZBcxWxw/mpmYbbHYBTcvIikalglolQadWIUCrUtQOvTa7QE1jM6obm1HVYEF1gwXVDc2oamhGdYMFVQ0WmBqtMDU2Ox4NFtfHduEIP+V15qu/kZ+SJECndkzz6ZzTfBoVdBrHnyO7XTimFRuBgk5+T9mbaS/+CyCEuOxfiuXLl2PZsmWuz2tqapCYmOjR+oiI/JFaJSFIpwEPkm5PrZIQHqxDeLAOyej8FLfdLlBnscLU0IyapmY0OUeQWn5tajOiZLe376Np7Z9xfB+baO23cf00bPm5KLV+COeYS+vnaP95m5+lnfkalSRBp1FBq3Y8dBoVdGqp3edatcoRRLStAaRtD5KmZVToampqamD8v527t7IFlaioKKjV6ktGT0pLSy8ZZXHS6/XQ67nVPREReReVqnX1F7mXbG3NOp0O48aNw+bNm9s9v3nzZkyZMkWmqoiIiMibyDr1s2zZMtx///1IS0vD5MmTsXLlSuTn5+PRRx+VsywiIiLyErIGlbvvvhsVFRV45ZVXUFxcjJSUFHzzzTdISkqSsywiIiLyErI30/7mN7/Bb37zG7nLICIiIi/ErfeIiIjIazGoEBERkddiUCEiIiKvxaBCREREXotBhYiIiLwWgwoRERF5LQYVIiIi8loMKkREROS1GFSIiIjIa8m+M21PCCEAOI6LJs+qt9QDTY6Pa2pqYNPZ5C2IiIh8lvPntvPn+JVIojNXeanCwkIkJibKXQYRERF1Q0FBARISEq54jU8HFbvdjvPnz8NgMECSJLnL8ZiamhokJiaioKAAoaGhcpcjK96LVrwXrXgvWvFetOK9cPDG+yCEQG1tLeLj46FSXbkLxaenflQq1VWTmD8JDQ31mj9kcuO9aMV70Yr3ohXvRSveCwdvuw9Go7FT17GZloiIiLwWgwoRERF5LQYVH6DX6/Hiiy9Cr9fLXYrseC9a8V604r1oxXvRivfCwdfvg0830xIREZF/44gKEREReS0GFSIiIvJaDCpERETktRhUiIiIyGsxqLjBzp07MW/ePMTHx0OSJGzYsKHd60IIvPTSS4iPj0dgYCCuv/56HD9+vN01ZrMZjz/+OKKiohAcHIzbbrsNhYWF7a6pqqrC/fffD6PRCKPRiPvvvx/V1dXtrsnPz8e8efMQHByMqKgoPPHEE7BYLO2uycrKwvTp0xEYGIi+ffvilVde6dR5C52Rnp6O8ePHw2AwIDo6GnfccQeys7MVeT9WrFiB0aNHuzZZmjx5Mr799lvF3YeLpaenQ5IkPPXUU67nlHIvXnrpJUiS1O4RGxuruPvgVFRUhPvuuw+RkZEICgrCNddcg8zMTMXdj/79+1/y50KSJCxZskRR9+GyBPXYN998I373u9+JL774QgAQ69evb/f6G2+8IQwGg/jiiy9EVlaWuPvuu0VcXJyoqalxXfPoo4+Kvn37is2bN4uDBw+KGTNmiDFjxgir1eq65uabbxYpKSli165dYteuXSIlJUXceuutrtetVqtISUkRM2bMEAcPHhSbN28W8fHxYunSpa5rTCaTiImJEffcc4/IysoSX3zxhTAYDOKtt95yy7246aabREZGhjh27Jg4fPiwmDt3rujXr5+oq6tT3P348ssvxddffy2ys7NFdna2eP7554VWqxXHjh1T1H1oa9++faJ///5i9OjR4sknn3Q9r5R78eKLL4qRI0eK4uJi16O0tFRx90EIISorK0VSUpJYvHix2Lt3rzh79qzYsmWLOH36tOLuR2lpabs/E5s3bxYAxLZt2xR1Hy6HQcXNLg4qdrtdxMbGijfeeMP1XFNTkzAajeKvf/2rEEKI6upqodVqxdq1a13XFBUVCZVKJb777jshhBAnTpwQAMSePXtc1+zevVsAED///LMQwhGYVCqVKCoqcl3z2WefCb1eL0wmkxBCiPfff18YjUbR1NTkuiY9PV3Ex8cLu93uxjvhUFpaKgCIHTt2CCF4P8LDw8Xf/vY3Rd6H2tpaMXjwYLF582Yxffp0V1BR0r148cUXxZgxYzp8TUn3QQghnn32WXHttdde9nWl3Y+2nnzySTFw4EBht9sVfR+cOPXjYWfPnkVJSQlmz57tek6v12P69OnYtWsXACAzMxPNzc3tromPj0dKSorrmt27d8NoNGLixImuayZNmgSj0djumpSUFMTHx7uuuemmm2A2m13Dqbt378b06dPbbfxz00034fz58zh37pzbf/8mkwkAEBERAUC598Nms2Ht2rWor6/H5MmTFXkflixZgrlz52LWrFntnlfavcjJyUF8fDySk5Nxzz33IDc3V5H34csvv0RaWhoWLFiA6OhopKamYtWqVa7XlXY/nCwWC9asWYOHHnoIkiQp9j60xaDiYSUlJQCAmJiYds/HxMS4XispKYFOp0N4ePgVr4mOjr7k+0dHR7e75uL3CQ8Ph06nu+I1zs+d17iLEALLli3Dtddei5SUlHbvoZT7kZWVhZCQEOj1ejz66KNYv349RowYobj7sHbtWhw8eBDp6emXvKakezFx4kSsXr0aGzduxKpVq1BSUoIpU6agoqJCUfcBAHJzc7FixQoMHjwYGzduxKOPPoonnngCq1evbvceSrkfThs2bEB1dTUWL17c7nsr7T605dOnJ/sSSZLafS6EuOS5i118TUfXu+Ma0dIEdbV6umrp0qU4evQofvzxx0teU8r9GDp0KA4fPozq6mp88cUXWLRoEXbs2HHF9/a3+1BQUIAnn3wSmzZtQkBAwGWvU8K9mDNnjuvjUaNGYfLkyRg4cCA+/vhjTJo06bLv7W/3AQDsdjvS0tLw+uuvAwBSU1Nx/PhxrFixAg888MAVa/DH++H04YcfYs6cOe1GNS733v58H9riiIqHOTv6L06apaWlrhQaGxsLi8WCqqqqK15z4cKFS75/WVlZu2sufp+qqio0Nzdf8ZrS0lIAlyb2nnj88cfx5ZdfYtu2bUhISHA9r7T7odPpMGjQIKSlpSE9PR1jxozBu+++q6j7kJmZidLSUowbNw4ajQYajQY7duzAn//8Z2g0msv+35g/3ouLBQcHY9SoUcjJyVHUnwkAiIuLw4gRI9o9N3z4cOTn57veH1DO/QCAvLw8bNmyBQ8//LDrOSXeh4sxqHhYcnIyYmNjsXnzZtdzFosFO3bswJQpUwAA48aNg1arbXdNcXExjh075rpm8uTJMJlM2Ldvn+uavXv3wmQytbvm2LFjKC4udl2zadMm6PV6jBs3znXNzp072y0327RpE+Lj49G/f/8e/36FEFi6dCnWrVuHrVu3Ijk5WdH342JCCJjNZkXdh5kzZyIrKwuHDx92PdLS0rBw4UIcPnwYAwYMUMy9uJjZbMbJkycRFxenqD8TADB16tRLti44deoUkpKSACjz34qMjAxER0dj7ty5rueUeB8u4ZEWXYWpra0Vhw4dEocOHRIAxDvvvCMOHTok8vLyhBCOpWVGo1GsW7dOZGVliXvvvbfDpWUJCQliy5Yt4uDBg+KGG27ocGnZ6NGjxe7du8Xu3bvFqFGjOlxaNnPmTHHw4EGxZcsWkZCQ0G5pWXV1tYiJiRH33nuvyMrKEuvWrROhoaFuW1r22GOPCaPRKLZv395uuV1DQ4PrGqXcj+XLl4udO3eKs2fPiqNHj4rnn39eqFQqsWnTJkXdh460XfWjpHvx9NNPi+3bt4vc3FyxZ88eceuttwqDwSDOnTunqPsghGOpukajEa+99prIyckRn3zyiQgKChJr1qxxXaOk+2Gz2US/fv3Es88+e8lrSroPHWFQcYNt27YJAJc8Fi1aJIRwLLN78cUXRWxsrNDr9eK6664TWVlZ7b5HY2OjWLp0qYiIiBCBgYHi1ltvFfn5+e2uqaioEAsXLhQGg0EYDAaxcOFCUVVV1e6avLw8MXfuXBEYGCgiIiLE0qVL2y0jE0KIo0ePimnTpgm9Xi9iY2PFSy+95LZlZR3dBwAiIyPDdY1S7sdDDz0kkpKShE6nE3369BEzZ850hRQl3YeOXBxUlHIvnPtfaLVaER8fL+bPny+OHz+uuPvg9NVXX4mUlBSh1+vFsGHDxMqVK9u9rqT7sXHjRgFAZGdnX/Kaku5DRyQhPLmdHBEREVH3sUeFiIiIvBaDChEREXktBhUiIiLyWgwqRERE5LUYVIiIiMhrMagQERGR12JQISIiIq/FoEJERERei0GFiIiIvBaDChEREXktBhUiIiLyWgwqRERE5LX+PxG92Z4ZM8owAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "houses['SalePrice'].plot.kde(xlim = (houses['SalePrice'].min(),\n",
    "                                  houses['SalePrice'].max()))\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.axvline(150000, color = 'Green')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This distribution is clearly right skewed. Generally, the location of the mode, median and mean is predictable for a right-skewed distribution:\n",
    "\n",
    "+ Most values are concentrated in the left body of the distribution where they will form a peak — this is where the mode will be.\n",
    "\n",
    "+ Remember that the median divides a distribution in two halves of equal length. For this reason, the median is usually positioned slightly right from the peak (the mode) for a right-skewed distribution.\n",
    "+ The mean takes into account each value in the distribution, and it will be affected by the outliers in the right tail. This will generally pull the mean to the right of the median.\n",
    "\n",
    "So in a right-skewed distribution, the mean will usually be to the right of the median, and the median will be to the right of the mode. This holds true for the distribution of the SalePrice variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f0746c91400>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "houses['SalePrice'].plot.kde(xlim = (houses['SalePrice'].min(),\n",
    "                                     houses['SalePrice'].max()\n",
    "                                    )\n",
    "                            )\n",
    "plt.axvline(150000, color = 'Green', label = 'Mode')\n",
    "plt.axvline(houses['SalePrice'].median(), color = 'Black', label = 'Median')\n",
    "plt.axvline(houses['SalePrice'].mean(), color = 'Orange', label = 'Mean')\n",
    "plt.legend()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task\n",
    "\n",
    "The distribution of the Mo Sold variable (which describes the month of a sale) is close to normal.\n",
    "+ Plot a kernel density plot for this distribution using Series.plot.kde().\n",
    "+ The lower boundary of the x-axis should be 1 and the upper one 12. You can use the xlim parameter of the Series.plot.kde() method.\n",
    "    + Plot three vertical lines:\n",
    "        + One for the mode — the color of the line should be green and its label should be 'Mode'.\n",
    "        + One for the median — the color of the line should be orange and its label should be 'Median'.\n",
    "        + One for the mean — the color of the line should be black and its label should be 'Mean'.\n",
    "+ Display all the labels using a legend (you can activate the legend using plt.legend().\n",
    "\n",
    "+ You should observe the mean, the median, and the mode clustered together in the center of the distribution.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f07498d80d0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "houses['Mo Sold'].plot.kde(xlim = (1,12))\n",
    "plt.axvline(6, color = 'Green', label = 'Mode')\n",
    "plt.axvline(houses['Mo Sold'].median(), color = 'Orange', label = 'Median')\n",
    "plt.axvline(houses['Mo Sold'].mean(), color = 'Black', label = 'Mean')\n",
    "plt.legend()\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Mean, Mode, Media](img/s2m3_summary.svg)"
   ]
  }
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