Descriptive Statistics_Education_Dataset.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "080ddb0a",
   "metadata": {},
   "source": [
    "# Descriptive Statististical Analysis: Grades Districts Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3e1d6ff",
   "metadata": {},
   "source": [
    "The following dataset contains information about various schools throughout various districts within a state. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9edd2c1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "import statsmodels.api as sm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7a23c00f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df= pd.read_csv('education_districtwise.csv')\n",
    "#drop the missing values:\n",
    "df= df.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e74573f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DISTNAME</th>\n",
       "      <th>STATNAME</th>\n",
       "      <th>BLOCKS</th>\n",
       "      <th>VILLAGES</th>\n",
       "      <th>CLUSTERS</th>\n",
       "      <th>TOTPOPULAT</th>\n",
       "      <th>OVERALL_LI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>DISTRICT32</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>13</td>\n",
       "      <td>391</td>\n",
       "      <td>104</td>\n",
       "      <td>875564.0</td>\n",
       "      <td>66.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>DISTRICT649</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>18</td>\n",
       "      <td>678</td>\n",
       "      <td>144</td>\n",
       "      <td>1015503.0</td>\n",
       "      <td>66.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>DISTRICT229</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>8</td>\n",
       "      <td>94</td>\n",
       "      <td>65</td>\n",
       "      <td>1269751.0</td>\n",
       "      <td>71.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>DISTRICT259</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>13</td>\n",
       "      <td>523</td>\n",
       "      <td>104</td>\n",
       "      <td>735753.0</td>\n",
       "      <td>57.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>DISTRICT486</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>8</td>\n",
       "      <td>359</td>\n",
       "      <td>64</td>\n",
       "      <td>570060.0</td>\n",
       "      <td>65.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      DISTNAME STATNAME  BLOCKS  VILLAGES  CLUSTERS  TOTPOPULAT  OVERALL_LI\n",
       "0   DISTRICT32   STATE1      13       391       104    875564.0       66.92\n",
       "1  DISTRICT649   STATE1      18       678       144   1015503.0       66.93\n",
       "2  DISTRICT229   STATE1       8        94        65   1269751.0       71.21\n",
       "3  DISTRICT259   STATE1      13       523       104    735753.0       57.98\n",
       "4  DISTRICT486   STATE1       8       359        64    570060.0       65.00"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "025228fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 634 entries, 0 to 679\n",
      "Data columns (total 7 columns):\n",
      " #   Column      Non-Null Count  Dtype  \n",
      "---  ------      --------------  -----  \n",
      " 0   DISTNAME    634 non-null    object \n",
      " 1   STATNAME    634 non-null    object \n",
      " 2   BLOCKS      634 non-null    int64  \n",
      " 3   VILLAGES    634 non-null    int64  \n",
      " 4   CLUSTERS    634 non-null    int64  \n",
      " 5   TOTPOPULAT  634 non-null    float64\n",
      " 6   OVERALL_LI  634 non-null    float64\n",
      "dtypes: float64(2), int64(3), object(2)\n",
      "memory usage: 39.6+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9700d38f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>BLOCKS</th>\n",
       "      <th>VILLAGES</th>\n",
       "      <th>CLUSTERS</th>\n",
       "      <th>TOTPOPULAT</th>\n",
       "      <th>OVERALL_LI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>634.000000</td>\n",
       "      <td>634.000000</td>\n",
       "      <td>634.000000</td>\n",
       "      <td>6.340000e+02</td>\n",
       "      <td>634.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>11.118297</td>\n",
       "      <td>899.619874</td>\n",
       "      <td>124.610410</td>\n",
       "      <td>1.899024e+06</td>\n",
       "      <td>73.395189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.799581</td>\n",
       "      <td>632.473675</td>\n",
       "      <td>95.821688</td>\n",
       "      <td>1.547475e+06</td>\n",
       "      <td>10.098460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>7.948000e+03</td>\n",
       "      <td>37.220000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>396.750000</td>\n",
       "      <td>60.000000</td>\n",
       "      <td>8.226940e+05</td>\n",
       "      <td>66.437500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>8.000000</td>\n",
       "      <td>816.500000</td>\n",
       "      <td>105.000000</td>\n",
       "      <td>1.564392e+06</td>\n",
       "      <td>73.490000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>13.000000</td>\n",
       "      <td>1231.500000</td>\n",
       "      <td>167.000000</td>\n",
       "      <td>2.587520e+06</td>\n",
       "      <td>80.815000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>66.000000</td>\n",
       "      <td>3963.000000</td>\n",
       "      <td>592.000000</td>\n",
       "      <td>1.105413e+07</td>\n",
       "      <td>98.760000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           BLOCKS     VILLAGES    CLUSTERS    TOTPOPULAT  OVERALL_LI\n",
       "count  634.000000   634.000000  634.000000  6.340000e+02  634.000000\n",
       "mean    11.118297   899.619874  124.610410  1.899024e+06   73.395189\n",
       "std      9.799581   632.473675   95.821688  1.547475e+06   10.098460\n",
       "min      1.000000     6.000000    1.000000  7.948000e+03   37.220000\n",
       "25%      6.000000   396.750000   60.000000  8.226940e+05   66.437500\n",
       "50%      8.000000   816.500000  105.000000  1.564392e+06   73.490000\n",
       "75%     13.000000  1231.500000  167.000000  2.587520e+06   80.815000\n",
       "max     66.000000  3963.000000  592.000000  1.105413e+07   98.760000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e3ffb48",
   "metadata": {},
   "source": [
    "#### We can use describe() to compute descriptive stats:\n",
    "\n",
    "1. count: Number of non-NA/null observations\n",
    "2. mean: The arithmetic average\n",
    "3. std: The standard deviation\n",
    "4. min: The smallest (minimum) value\n",
    "5. 25%: The first quartile (25th percentile)\n",
    "6. 50%: The median (50th percentile)\n",
    "7. 75%: The third quartile (75th percentile)\n",
    "8. max: The largest (maximum) value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6844971f",
   "metadata": {},
   "source": [
    "The summary of stats gives us valuable information about the overall literacy rate. For example, the mean helps to clarify the center of your dataset; we now know the average literacy rate is about 73% for all districts. This information is useful in itself and also as a basis for comparison. Knowing the mean literacy rate for all districts helps us understand which individual districts are significantly above or below the mean.\n",
    "\n",
    "Note: describe() excludes missing values (NaN) in the dataset from consideration. You may notice that the count, or the number of observations for OVERALL_LI (634), is fewer than the number of rows in the dataset (680). Dealing with missing values is a complex issue outside the scope of this course.\n",
    "\n",
    "You can also use the describe() function for a column with categorical data, like the STATNAME column.\n",
    "\n",
    "For a categorical column, describe() gives you the following output:\n",
    "\n",
    "count: Number of non-NA/null observations\n",
    "unique: Number of unique values\n",
    "top: The most common value (the mode)\n",
    "freq: The frequency of the most common value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6a2e6537",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count         634\n",
       "unique         36\n",
       "top       STATE21\n",
       "freq           71\n",
       "Name: STATNAME, dtype: object"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['STATNAME'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "807c292f",
   "metadata": {},
   "source": [
    "Data reveals that there are 35 unique states. The top catergory is State21 or value with most occurance/mode and freq tells us that there are 75 occurances of State21."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e2dd95de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61.540000000000006"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Compute range:\n",
    "range_overall_li = df['OVERALL_LI'].max() - df['OVERALL_LI'].min()\n",
    "range_overall_li\n",
    "#61.54"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e485cca",
   "metadata": {},
   "source": [
    "The range in literacy rates for all districts is about 61.5 percentage points.\n",
    "\n",
    "This large difference tells you that some districts have much higher literacy rates than others."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e33cc1ee",
   "metadata": {},
   "source": [
    "#### Visualization\n",
    "We will take a look at the probability distribution using a histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b83495c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 9,
     "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": [
    "df['OVERALL_LI'].hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bda14ae",
   "metadata": {},
   "source": [
    "The histogram shows that the literacy reate is nomrally disbruted since there is a bell shape curve with the mean being around 73%."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e15620d",
   "metadata": {},
   "source": [
    "#### Empirical rule\n",
    "\n",
    "Since the normal distribution seems like a good fit for the district literacy rate data, we can expect the empirical rule to apply relatively well. Recall that the empirical rule says that for a normal distribution:\n",
    "\n",
    "68% of the values fall within +/- 1 SD from the mean\n",
    "95% of the values fall within +/- 2 SD from the mean\n",
    "99.7% of the values fall within +/- 3 SD from the mean\n",
    "\n",
    "NOTE: \"SD\" stands for standard deviation.\n",
    "\n",
    "In other words, we can expect that about:\n",
    "\n",
    "68% of district literacy rates will fall within +/- 1 SD from the mean.\n",
    "95% of district literacy rates will fall within +/- 2 SD from the mean.\n",
    "99.7% of district literacy rates will fall within +/- 3 SD from the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4d9d3ab2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73.39518927444797"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#mean\n",
    "df_mean = df['OVERALL_LI'].mean()\n",
    "df_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a705b79d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.098460413782469"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#standard deviation\n",
    "df_std= df['OVERALL_LI'].std()\n",
    "df_std"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "836cd59d",
   "metadata": {},
   "source": [
    "We can observe a lower limit and upper limit 1 std away from the mean with lower limit being < than 1 std below mean, and upper limit  1 std/ > or above the mean.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f7f87416",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6640378548895899"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower_limit = df_mean -1 * df_std\n",
    "upper_limit = df_mean +1 * df_std\n",
    "((df['OVERALL_LI'] >= lower_limit) & (df['OVERALL_LI'] <= upper_limit)).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daa60013",
   "metadata": {},
   "source": [
    "We will do this with 2 std away from the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "592fd234",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9542586750788643"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower_limit = df_mean -2 * df_std\n",
    "upper_limit = df_mean +2 * df_std\n",
    "((df['OVERALL_LI'] >= lower_limit) & (df['OVERALL_LI'] <= upper_limit)).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10d5e3e9",
   "metadata": {},
   "source": [
    "The values agree quite well with the empirical rule.\n",
    "\n",
    "Our values of 66.4%, 95.4%, and 99.6% are very close to the values the empirical rule suggests: roughly 68%, 95%, and 99.7%."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb7f3b7f",
   "metadata": {},
   "source": [
    "We will find the z score o meanture how many standard deviations below or above the poluplation mean a data point is. This is helpful for detecing outliers, for instance. Any standard deviation 3 and up is going to be an outlier, more than likely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "152aa6c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DISTNAME</th>\n",
       "      <th>STATNAME</th>\n",
       "      <th>BLOCKS</th>\n",
       "      <th>VILLAGES</th>\n",
       "      <th>CLUSTERS</th>\n",
       "      <th>TOTPOPULAT</th>\n",
       "      <th>OVERALL_LI</th>\n",
       "      <th>Z_SCORE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>DISTRICT32</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>13</td>\n",
       "      <td>391</td>\n",
       "      <td>104</td>\n",
       "      <td>875564.0</td>\n",
       "      <td>66.92</td>\n",
       "      <td>-0.641712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>DISTRICT649</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>18</td>\n",
       "      <td>678</td>\n",
       "      <td>144</td>\n",
       "      <td>1015503.0</td>\n",
       "      <td>66.93</td>\n",
       "      <td>-0.640721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>DISTRICT229</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>8</td>\n",
       "      <td>94</td>\n",
       "      <td>65</td>\n",
       "      <td>1269751.0</td>\n",
       "      <td>71.21</td>\n",
       "      <td>-0.216559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>DISTRICT259</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>13</td>\n",
       "      <td>523</td>\n",
       "      <td>104</td>\n",
       "      <td>735753.0</td>\n",
       "      <td>57.98</td>\n",
       "      <td>-1.527694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>DISTRICT486</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>8</td>\n",
       "      <td>359</td>\n",
       "      <td>64</td>\n",
       "      <td>570060.0</td>\n",
       "      <td>65.00</td>\n",
       "      <td>-0.831990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>675</th>\n",
       "      <td>DISTRICT522</td>\n",
       "      <td>STATE29</td>\n",
       "      <td>37</td>\n",
       "      <td>876</td>\n",
       "      <td>137</td>\n",
       "      <td>5296396.0</td>\n",
       "      <td>78.05</td>\n",
       "      <td>0.461307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>DISTRICT498</td>\n",
       "      <td>STATE29</td>\n",
       "      <td>64</td>\n",
       "      <td>1458</td>\n",
       "      <td>230</td>\n",
       "      <td>4042191.0</td>\n",
       "      <td>56.06</td>\n",
       "      <td>-1.717972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>677</th>\n",
       "      <td>DISTRICT343</td>\n",
       "      <td>STATE29</td>\n",
       "      <td>59</td>\n",
       "      <td>1117</td>\n",
       "      <td>216</td>\n",
       "      <td>3483648.0</td>\n",
       "      <td>65.05</td>\n",
       "      <td>-0.827035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>678</th>\n",
       "      <td>DISTRICT130</td>\n",
       "      <td>STATE29</td>\n",
       "      <td>51</td>\n",
       "      <td>993</td>\n",
       "      <td>211</td>\n",
       "      <td>3522644.0</td>\n",
       "      <td>66.16</td>\n",
       "      <td>-0.717030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>679</th>\n",
       "      <td>DISTRICT341</td>\n",
       "      <td>STATE29</td>\n",
       "      <td>41</td>\n",
       "      <td>783</td>\n",
       "      <td>185</td>\n",
       "      <td>2798214.0</td>\n",
       "      <td>65.46</td>\n",
       "      <td>-0.786403</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>634 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        DISTNAME STATNAME  BLOCKS  VILLAGES  CLUSTERS  TOTPOPULAT  OVERALL_LI  \\\n",
       "0     DISTRICT32   STATE1      13       391       104    875564.0       66.92   \n",
       "1    DISTRICT649   STATE1      18       678       144   1015503.0       66.93   \n",
       "2    DISTRICT229   STATE1       8        94        65   1269751.0       71.21   \n",
       "3    DISTRICT259   STATE1      13       523       104    735753.0       57.98   \n",
       "4    DISTRICT486   STATE1       8       359        64    570060.0       65.00   \n",
       "..           ...      ...     ...       ...       ...         ...         ...   \n",
       "675  DISTRICT522  STATE29      37       876       137   5296396.0       78.05   \n",
       "676  DISTRICT498  STATE29      64      1458       230   4042191.0       56.06   \n",
       "677  DISTRICT343  STATE29      59      1117       216   3483648.0       65.05   \n",
       "678  DISTRICT130  STATE29      51       993       211   3522644.0       66.16   \n",
       "679  DISTRICT341  STATE29      41       783       185   2798214.0       65.46   \n",
       "\n",
       "      Z_SCORE  \n",
       "0   -0.641712  \n",
       "1   -0.640721  \n",
       "2   -0.216559  \n",
       "3   -1.527694  \n",
       "4   -0.831990  \n",
       "..        ...  \n",
       "675  0.461307  \n",
       "676 -1.717972  \n",
       "677 -0.827035  \n",
       "678 -0.717030  \n",
       "679 -0.786403  \n",
       "\n",
       "[634 rows x 8 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Z_SCORE'] = stats.zscore(df['OVERALL_LI'])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ad0416d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>DISTNAME</th>\n",
       "      <th>STATNAME</th>\n",
       "      <th>BLOCKS</th>\n",
       "      <th>VILLAGES</th>\n",
       "      <th>CLUSTERS</th>\n",
       "      <th>TOTPOPULAT</th>\n",
       "      <th>OVERALL_LI</th>\n",
       "      <th>Z_SCORE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>434</th>\n",
       "      <td>DISTRICT461</td>\n",
       "      <td>STATE31</td>\n",
       "      <td>4</td>\n",
       "      <td>360</td>\n",
       "      <td>53</td>\n",
       "      <td>532791.0</td>\n",
       "      <td>42.67</td>\n",
       "      <td>-3.044964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>DISTRICT429</td>\n",
       "      <td>STATE22</td>\n",
       "      <td>6</td>\n",
       "      <td>612</td>\n",
       "      <td>62</td>\n",
       "      <td>728677.0</td>\n",
       "      <td>37.22</td>\n",
       "      <td>-3.585076</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        DISTNAME STATNAME  BLOCKS  VILLAGES  CLUSTERS  TOTPOPULAT  OVERALL_LI  \\\n",
       "434  DISTRICT461  STATE31       4       360        53    532791.0       42.67   \n",
       "494  DISTRICT429  STATE22       6       612        62    728677.0       37.22   \n",
       "\n",
       "      Z_SCORE  \n",
       "434 -3.044964  \n",
       "494 -3.585076  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#calculate 3 std above and below mean:\n",
    "df[(df['Z_SCORE'] > 3) | (df['Z_SCORE'] < -3)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b80a3ed",
   "metadata": {},
   "source": [
    " There are two outliers. DISTRICT461 and DISTRICT429. The literacy rates in these two districts are more than 3 SDs below the overall mean literacy rate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ad69031",
   "metadata": {},
   "source": [
    "## Example of sampling distribution:\n",
    "We want to data on district literacy rates but are only using a portion of the population.\n",
    "\n",
    " - Total number of districts in sample:634 (see df.info)\n",
    " - random sample of 50 using .sample(n, replace, random_state) from pandas\n",
    "     - n refers to the desired sample size.\n",
    "     - replace indicates whether you are sampling with or without replacement.\n",
    " - random_state refers to the seed/starting point of the random number which can be any number.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bb7a4904",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>Z_SCORE</th>\n",
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       "  <tbody>\n",
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       "      <th>661</th>\n",
       "      <td>DISTRICT528</td>\n",
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       "      <td>9</td>\n",
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       "      <td>89</td>\n",
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       "      <td>92.14</td>\n",
       "      <td>1.857670</td>\n",
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       "      <th>216</th>\n",
       "      <td>DISTRICT291</td>\n",
       "      <td>STATE28</td>\n",
       "      <td>14</td>\n",
       "      <td>1188</td>\n",
       "      <td>165</td>\n",
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       "      <td>52.49</td>\n",
       "      <td>-2.071771</td>\n",
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       "      <th>367</th>\n",
       "      <td>DISTRICT66</td>\n",
       "      <td>STATE23</td>\n",
       "      <td>12</td>\n",
       "      <td>1169</td>\n",
       "      <td>116</td>\n",
       "      <td>1042304.0</td>\n",
       "      <td>62.14</td>\n",
       "      <td>-1.115425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>254</th>\n",
       "      <td>DISTRICT458</td>\n",
       "      <td>STATE3</td>\n",
       "      <td>3</td>\n",
       "      <td>157</td>\n",
       "      <td>19</td>\n",
       "      <td>82839.0</td>\n",
       "      <td>76.33</td>\n",
       "      <td>0.290849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>286</th>\n",
       "      <td>DISTRICT636</td>\n",
       "      <td>STATE35</td>\n",
       "      <td>3</td>\n",
       "      <td>187</td>\n",
       "      <td>44</td>\n",
       "      <td>514683.0</td>\n",
       "      <td>86.70</td>\n",
       "      <td>1.318549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>369</th>\n",
       "      <td>DISTRICT512</td>\n",
       "      <td>STATE23</td>\n",
       "      <td>6</td>\n",
       "      <td>589</td>\n",
       "      <td>30</td>\n",
       "      <td>717169.0</td>\n",
       "      <td>68.35</td>\n",
       "      <td>-0.499994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>258</th>\n",
       "      <td>DISTRICT156</td>\n",
       "      <td>STATE3</td>\n",
       "      <td>6</td>\n",
       "      <td>80</td>\n",
       "      <td>9</td>\n",
       "      <td>35289.0</td>\n",
       "      <td>59.94</td>\n",
       "      <td>-1.333452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>DISTRICT412</td>\n",
       "      <td>STATE1</td>\n",
       "      <td>11</td>\n",
       "      <td>187</td>\n",
       "      <td>95</td>\n",
       "      <td>476820.0</td>\n",
       "      <td>68.69</td>\n",
       "      <td>-0.466299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>512</th>\n",
       "      <td>DISTRICT277</td>\n",
       "      <td>STATE9</td>\n",
       "      <td>10</td>\n",
       "      <td>558</td>\n",
       "      <td>179</td>\n",
       "      <td>2298934.0</td>\n",
       "      <td>84.31</td>\n",
       "      <td>1.081692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>DISTRICT133</td>\n",
       "      <td>STATE21</td>\n",
       "      <td>14</td>\n",
       "      <td>1672</td>\n",
       "      <td>136</td>\n",
       "      <td>3673849.0</td>\n",
       "      <td>69.61</td>\n",
       "      <td>-0.375124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>325</th>\n",
       "      <td>DISTRICT1</td>\n",
       "      <td>STATE33</td>\n",
       "      <td>4</td>\n",
       "      <td>534</td>\n",
       "      <td>98</td>\n",
       "      <td>957853.0</td>\n",
       "      <td>69.37</td>\n",
       "      <td>-0.398909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>227</th>\n",
       "      <td>DISTRICT159</td>\n",
       "      <td>STATE28</td>\n",
       "      <td>18</td>\n",
       "      <td>870</td>\n",
       "      <td>134</td>\n",
       "      <td>2954367.0</td>\n",
       "      <td>66.23</td>\n",
       "      <td>-0.710093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>DISTRICT667</td>\n",
       "      <td>STATE25</td>\n",
       "      <td>5</td>\n",
       "      <td>396</td>\n",
       "      <td>75</td>\n",
       "      <td>896129.0</td>\n",
       "      <td>82.23</td>\n",
       "      <td>0.875558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>425</th>\n",
       "      <td>DISTRICT144</td>\n",
       "      <td>STATE31</td>\n",
       "      <td>7</td>\n",
       "      <td>1064</td>\n",
       "      <td>108</td>\n",
       "      <td>2662077.0</td>\n",
       "      <td>71.59</td>\n",
       "      <td>-0.178900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>260</th>\n",
       "      <td>DISTRICT305</td>\n",
       "      <td>STATE3</td>\n",
       "      <td>2</td>\n",
       "      <td>62</td>\n",
       "      <td>6</td>\n",
       "      <td>145538.0</td>\n",
       "      <td>69.88</td>\n",
       "      <td>-0.348366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>281</th>\n",
       "      <td>DISTRICT385</td>\n",
       "      <td>STATE35</td>\n",
       "      <td>6</td>\n",
       "      <td>531</td>\n",
       "      <td>30</td>\n",
       "      <td>354972.0</td>\n",
       "      <td>75.00</td>\n",
       "      <td>0.159042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>262</th>\n",
       "      <td>DISTRICT552</td>\n",
       "      <td>STATE3</td>\n",
       "      <td>3</td>\n",
       "      <td>103</td>\n",
       "      <td>4</td>\n",
       "      <td>111997.0</td>\n",
       "      <td>52.23</td>\n",
       "      <td>-2.097538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>253</th>\n",
       "      <td>DISTRICT168</td>\n",
       "      <td>STATE3</td>\n",
       "      <td>5</td>\n",
       "      <td>312</td>\n",
       "      <td>16</td>\n",
       "      <td>176385.0</td>\n",
       "      <td>82.14</td>\n",
       "      <td>0.866639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>301</th>\n",
       "      <td>DISTRICT551</td>\n",
       "      <td>STATE14</td>\n",
       "      <td>9</td>\n",
       "      <td>103</td>\n",
       "      <td>63</td>\n",
       "      <td>693281.0</td>\n",
       "      <td>88.29</td>\n",
       "      <td>1.476123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>356</th>\n",
       "      <td>DISTRICT494</td>\n",
       "      <td>STATE34</td>\n",
       "      <td>25</td>\n",
       "      <td>2179</td>\n",
       "      <td>223</td>\n",
       "      <td>3596292.0</td>\n",
       "      <td>70.95</td>\n",
       "      <td>-0.242326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>165</th>\n",
       "      <td>DISTRICT196</td>\n",
       "      <td>STATE21</td>\n",
       "      <td>10</td>\n",
       "      <td>1354</td>\n",
       "      <td>119</td>\n",
       "      <td>1795092.0</td>\n",
       "      <td>77.52</td>\n",
       "      <td>0.408782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>565</th>\n",
       "      <td>DISTRICT308</td>\n",
       "      <td>STATE17</td>\n",
       "      <td>8</td>\n",
       "      <td>721</td>\n",
       "      <td>144</td>\n",
       "      <td>848868.0</td>\n",
       "      <td>86.54</td>\n",
       "      <td>1.302693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>388</th>\n",
       "      <td>DISTRICT281</td>\n",
       "      <td>STATE23</td>\n",
       "      <td>6</td>\n",
       "      <td>392</td>\n",
       "      <td>58</td>\n",
       "      <td>949159.0</td>\n",
       "      <td>73.92</td>\n",
       "      <td>0.052010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>461</th>\n",
       "      <td>DISTRICT619</td>\n",
       "      <td>STATE22</td>\n",
       "      <td>5</td>\n",
       "      <td>859</td>\n",
       "      <td>57</td>\n",
       "      <td>1064989.0</td>\n",
       "      <td>68.36</td>\n",
       "      <td>-0.499003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>384</th>\n",
       "      <td>DISTRICT455</td>\n",
       "      <td>STATE23</td>\n",
       "      <td>9</td>\n",
       "      <td>1217</td>\n",
       "      <td>55</td>\n",
       "      <td>1063458.0</td>\n",
       "      <td>68.85</td>\n",
       "      <td>-0.450443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>590</th>\n",
       "      <td>DISTRICT70</td>\n",
       "      <td>STATE20</td>\n",
       "      <td>7</td>\n",
       "      <td>427</td>\n",
       "      <td>84</td>\n",
       "      <td>1846993.0</td>\n",
       "      <td>80.30</td>\n",
       "      <td>0.684289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>343</th>\n",
       "      <td>DISTRICT354</td>\n",
       "      <td>STATE33</td>\n",
       "      <td>2</td>\n",
       "      <td>192</td>\n",
       "      <td>46</td>\n",
       "      <td>1260419.0</td>\n",
       "      <td>88.66</td>\n",
       "      <td>1.512791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>539</th>\n",
       "      <td>DISTRICT440</td>\n",
       "      <td>STATE17</td>\n",
       "      <td>15</td>\n",
       "      <td>1465</td>\n",
       "      <td>167</td>\n",
       "      <td>2887826.0</td>\n",
       "      <td>88.23</td>\n",
       "      <td>1.470177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>459</th>\n",
       "      <td>DISTRICT431</td>\n",
       "      <td>STATE22</td>\n",
       "      <td>9</td>\n",
       "      <td>1778</td>\n",
       "      <td>143</td>\n",
       "      <td>2363744.0</td>\n",
       "      <td>73.42</td>\n",
       "      <td>0.002459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>667</th>\n",
       "      <td>DISTRICT123</td>\n",
       "      <td>STATE11</td>\n",
       "      <td>3</td>\n",
       "      <td>80</td>\n",
       "      <td>16</td>\n",
       "      <td>237586.0</td>\n",
       "      <td>88.49</td>\n",
       "      <td>1.495944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>387</th>\n",
       "      <td>DISTRICT231</td>\n",
       "      <td>STATE23</td>\n",
       "      <td>6</td>\n",
       "      <td>657</td>\n",
       "      <td>63</td>\n",
       "      <td>530299.0</td>\n",
       "      <td>64.51</td>\n",
       "      <td>-0.880551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>306</th>\n",
       "      <td>DISTRICT37</td>\n",
       "      <td>STATE4</td>\n",
       "      <td>7</td>\n",
       "      <td>1083</td>\n",
       "      <td>92</td>\n",
       "      <td>642923.0</td>\n",
       "      <td>68.38</td>\n",
       "      <td>-0.497021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>213</th>\n",
       "      <td>DISTRICT347</td>\n",
       "      <td>STATE28</td>\n",
       "      <td>11</td>\n",
       "      <td>623</td>\n",
       "      <td>94</td>\n",
       "      <td>2228397.0</td>\n",
       "      <td>59.65</td>\n",
       "      <td>-1.362192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>DISTRICT22</td>\n",
       "      <td>STATE2</td>\n",
       "      <td>7</td>\n",
       "      <td>182</td>\n",
       "      <td>7</td>\n",
       "      <td>2531583.0</td>\n",
       "      <td>87.12</td>\n",
       "      <td>1.360172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>DISTRICT247</td>\n",
       "      <td>STATE25</td>\n",
       "      <td>7</td>\n",
       "      <td>314</td>\n",
       "      <td>60</td>\n",
       "      <td>1332042.0</td>\n",
       "      <td>72.73</td>\n",
       "      <td>-0.065922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>394</th>\n",
       "      <td>DISTRICT640</td>\n",
       "      <td>STATE24</td>\n",
       "      <td>17</td>\n",
       "      <td>1857</td>\n",
       "      <td>191</td>\n",
       "      <td>1802777.0</td>\n",
       "      <td>69.00</td>\n",
       "      <td>-0.435577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>184</th>\n",
       "      <td>DISTRICT596</td>\n",
       "      <td>STATE21</td>\n",
       "      <td>11</td>\n",
       "      <td>1281</td>\n",
       "      <td>108</td>\n",
       "      <td>2149066.0</td>\n",
       "      <td>51.76</td>\n",
       "      <td>-2.144116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>DISTRICT335</td>\n",
       "      <td>STATE21</td>\n",
       "      <td>17</td>\n",
       "      <td>1945</td>\n",
       "      <td>138</td>\n",
       "      <td>4380793.0</td>\n",
       "      <td>69.44</td>\n",
       "      <td>-0.391972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>542</th>\n",
       "      <td>DISTRICT489</td>\n",
       "      <td>STATE17</td>\n",
       "      <td>7</td>\n",
       "      <td>749</td>\n",
       "      <td>63</td>\n",
       "      <td>1198810.0</td>\n",
       "      <td>85.14</td>\n",
       "      <td>1.163948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>105</th>\n",
       "      <td>DISTRICT157</td>\n",
       "      <td>STATE13</td>\n",
       "      <td>14</td>\n",
       "      <td>1994</td>\n",
       "      <td>508</td>\n",
       "      <td>3671999.0</td>\n",
       "      <td>71.68</td>\n",
       "      <td>-0.169981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>254</th>\n",
       "      <td>DISTRICT458</td>\n",
       "      <td>STATE3</td>\n",
       "      <td>3</td>\n",
       "      <td>157</td>\n",
       "      <td>19</td>\n",
       "      <td>82839.0</td>\n",
       "      <td>76.33</td>\n",
       "      <td>0.290849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>DISTRICT158</td>\n",
       "      <td>STATE13</td>\n",
       "      <td>6</td>\n",
       "      <td>769</td>\n",
       "      <td>211</td>\n",
       "      <td>1338114.0</td>\n",
       "      <td>66.19</td>\n",
       "      <td>-0.714057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>609</th>\n",
       "      <td>DISTRICT17</td>\n",
       "      <td>STATE20</td>\n",
       "      <td>4</td>\n",
       "      <td>359</td>\n",
       "      <td>59</td>\n",
       "      <td>9588910.0</td>\n",
       "      <td>88.48</td>\n",
       "      <td>1.494953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>DISTRICT126</td>\n",
       "      <td>STATE26</td>\n",
       "      <td>3</td>\n",
       "      <td>197</td>\n",
       "      <td>21</td>\n",
       "      <td>596294.0</td>\n",
       "      <td>68.90</td>\n",
       "      <td>-0.445488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>DISTRICT45</td>\n",
       "      <td>STATE25</td>\n",
       "      <td>9</td>\n",
       "      <td>351</td>\n",
       "      <td>130</td>\n",
       "      <td>1742815.0</td>\n",
       "      <td>73.24</td>\n",
       "      <td>-0.015380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>516</th>\n",
       "      <td>DISTRICT300</td>\n",
       "      <td>STATE9</td>\n",
       "      <td>5</td>\n",
       "      <td>651</td>\n",
       "      <td>84</td>\n",
       "      <td>590379.0</td>\n",
       "      <td>73.29</td>\n",
       "      <td>-0.010425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>641</th>\n",
       "      <td>DISTRICT484</td>\n",
       "      <td>STATE6</td>\n",
       "      <td>15</td>\n",
       "      <td>333</td>\n",
       "      <td>83</td>\n",
       "      <td>1721179.0</td>\n",
       "      <td>74.92</td>\n",
       "      <td>0.151114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>650</th>\n",
       "      <td>DISTRICT145</td>\n",
       "      <td>STATE6</td>\n",
       "      <td>11</td>\n",
       "      <td>489</td>\n",
       "      <td>100</td>\n",
       "      <td>1614069.0</td>\n",
       "      <td>84.09</td>\n",
       "      <td>1.059890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>DISTRICT99</td>\n",
       "      <td>STATE25</td>\n",
       "      <td>4</td>\n",
       "      <td>279</td>\n",
       "      <td>43</td>\n",
       "      <td>558890.0</td>\n",
       "      <td>83.44</td>\n",
       "      <td>0.995473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>163</th>\n",
       "      <td>DISTRICT366</td>\n",
       "      <td>STATE21</td>\n",
       "      <td>9</td>\n",
       "      <td>1330</td>\n",
       "      <td>86</td>\n",
       "      <td>1579160.0</td>\n",
       "      <td>79.99</td>\n",
       "      <td>0.653567</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        DISTNAME STATNAME  BLOCKS  VILLAGES  CLUSTERS  TOTPOPULAT  OVERALL_LI  \\\n",
       "661  DISTRICT528   STATE6       9       112        89   1863174.0       92.14   \n",
       "216  DISTRICT291  STATE28      14      1188       165   3273127.0       52.49   \n",
       "367   DISTRICT66  STATE23      12      1169       116   1042304.0       62.14   \n",
       "254  DISTRICT458   STATE3       3       157        19     82839.0       76.33   \n",
       "286  DISTRICT636  STATE35       3       187        44    514683.0       86.70   \n",
       "369  DISTRICT512  STATE23       6       589        30    717169.0       68.35   \n",
       "258  DISTRICT156   STATE3       6        80         9     35289.0       59.94   \n",
       "10   DISTRICT412   STATE1      11       187        95    476820.0       68.69   \n",
       "512  DISTRICT277   STATE9      10       558       179   2298934.0       84.31   \n",
       "144  DISTRICT133  STATE21      14      1672       136   3673849.0       69.61   \n",
       "325    DISTRICT1  STATE33       4       534        98    957853.0       69.37   \n",
       "227  DISTRICT159  STATE28      18       870       134   2954367.0       66.23   \n",
       "86   DISTRICT667  STATE25       5       396        75    896129.0       82.23   \n",
       "425  DISTRICT144  STATE31       7      1064       108   2662077.0       71.59   \n",
       "260  DISTRICT305   STATE3       2        62         6    145538.0       69.88   \n",
       "281  DISTRICT385  STATE35       6       531        30    354972.0       75.00   \n",
       "262  DISTRICT552   STATE3       3       103         4    111997.0       52.23   \n",
       "253  DISTRICT168   STATE3       5       312        16    176385.0       82.14   \n",
       "301  DISTRICT551  STATE14       9       103        63    693281.0       88.29   \n",
       "356  DISTRICT494  STATE34      25      2179       223   3596292.0       70.95   \n",
       "165  DISTRICT196  STATE21      10      1354       119   1795092.0       77.52   \n",
       "565  DISTRICT308  STATE17       8       721       144    848868.0       86.54   \n",
       "388  DISTRICT281  STATE23       6       392        58    949159.0       73.92   \n",
       "461  DISTRICT619  STATE22       5       859        57   1064989.0       68.36   \n",
       "384  DISTRICT455  STATE23       9      1217        55   1063458.0       68.85   \n",
       "590   DISTRICT70  STATE20       7       427        84   1846993.0       80.30   \n",
       "343  DISTRICT354  STATE33       2       192        46   1260419.0       88.66   \n",
       "539  DISTRICT440  STATE17      15      1465       167   2887826.0       88.23   \n",
       "459  DISTRICT431  STATE22       9      1778       143   2363744.0       73.42   \n",
       "667  DISTRICT123  STATE11       3        80        16    237586.0       88.49   \n",
       "387  DISTRICT231  STATE23       6       657        63    530299.0       64.51   \n",
       "306   DISTRICT37   STATE4       7      1083        92    642923.0       68.38   \n",
       "213  DISTRICT347  STATE28      11       623        94   2228397.0       59.65   \n",
       "97    DISTRICT22   STATE2       7       182         7   2531583.0       87.12   \n",
       "78   DISTRICT247  STATE25       7       314        60   1332042.0       72.73   \n",
       "394  DISTRICT640  STATE24      17      1857       191   1802777.0       69.00   \n",
       "184  DISTRICT596  STATE21      11      1281       108   2149066.0       51.76   \n",
       "147  DISTRICT335  STATE21      17      1945       138   4380793.0       69.44   \n",
       "542  DISTRICT489  STATE17       7       749        63   1198810.0       85.14   \n",
       "105  DISTRICT157  STATE13      14      1994       508   3671999.0       71.68   \n",
       "254  DISTRICT458   STATE3       3       157        19     82839.0       76.33   \n",
       "109  DISTRICT158  STATE13       6       769       211   1338114.0       66.19   \n",
       "609   DISTRICT17  STATE20       4       359        59   9588910.0       88.48   \n",
       "53   DISTRICT126  STATE26       3       197        21    596294.0       68.90   \n",
       "81    DISTRICT45  STATE25       9       351       130   1742815.0       73.24   \n",
       "516  DISTRICT300   STATE9       5       651        84    590379.0       73.29   \n",
       "641  DISTRICT484   STATE6      15       333        83   1721179.0       74.92   \n",
       "650  DISTRICT145   STATE6      11       489       100   1614069.0       84.09   \n",
       "70    DISTRICT99  STATE25       4       279        43    558890.0       83.44   \n",
       "163  DISTRICT366  STATE21       9      1330        86   1579160.0       79.99   \n",
       "\n",
       "      Z_SCORE  \n",
       "661  1.857670  \n",
       "216 -2.071771  \n",
       "367 -1.115425  \n",
       "254  0.290849  \n",
       "286  1.318549  \n",
       "369 -0.499994  \n",
       "258 -1.333452  \n",
       "10  -0.466299  \n",
       "512  1.081692  \n",
       "144 -0.375124  \n",
       "325 -0.398909  \n",
       "227 -0.710093  \n",
       "86   0.875558  \n",
       "425 -0.178900  \n",
       "260 -0.348366  \n",
       "281  0.159042  \n",
       "262 -2.097538  \n",
       "253  0.866639  \n",
       "301  1.476123  \n",
       "356 -0.242326  \n",
       "165  0.408782  \n",
       "565  1.302693  \n",
       "388  0.052010  \n",
       "461 -0.499003  \n",
       "384 -0.450443  \n",
       "590  0.684289  \n",
       "343  1.512791  \n",
       "539  1.470177  \n",
       "459  0.002459  \n",
       "667  1.495944  \n",
       "387 -0.880551  \n",
       "306 -0.497021  \n",
       "213 -1.362192  \n",
       "97   1.360172  \n",
       "78  -0.065922  \n",
       "394 -0.435577  \n",
       "184 -2.144116  \n",
       "147 -0.391972  \n",
       "542  1.163948  \n",
       "105 -0.169981  \n",
       "254  0.290849  \n",
       "109 -0.714057  \n",
       "609  1.494953  \n",
       "53  -0.445488  \n",
       "81  -0.015380  \n",
       "516 -0.010425  \n",
       "641  0.151114  \n",
       "650  1.059890  \n",
       "70   0.995473  \n",
       "163  0.653567  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_data= df.sample(n=50, replace=True, random_state =31208)\n",
    "sample_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "003f9209",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74.22359999999999"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We want to calculate the mean of the sample data: 74.22\n",
    "estimate1 = sample_data['OVERALL_LI'].mean()\n",
    "estimate1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0338f393",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74.24780000000001"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#compare mean of sample:74.24\n",
    "estimate2 = df['OVERALL_LI'].sample(n=50, replace=True, random_state= 56810).mean()\n",
    "estimate2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f347c4ef",
   "metadata": {},
   "source": [
    "#### Centrail Limit Theorem\n",
    "\n",
    "This theorem states that when data is large enough, the mean of the sample data will match that of the larger population. Both saamples are really close.\n",
    "\n",
    "We should also observe a normal distribution pattern/bell cuve where the mean is nearly identicle to population mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a26b93a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 19,
     "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": [
    "sample_data[\"OVERALL_LI\"].hist(rwidth=0.9)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8736b17e",
   "metadata": {},
   "source": [
    "As we can see, the mode or most occurance lies around 70 which reflect the population mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "25e3868b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#you can also check the mean for a random sample like this:\n",
    "#changing the sample size changes the result/mean, with greater number being more accurate.\n",
    "\n",
    "estimate_list =[]\n",
    "for i in range(10000):\n",
    "    estimate_list.append(df['OVERALL_LI'].sample(n=50, replace=True).mean())\n",
    "estimate_df= pd.DataFrame(data={'estimate': estimate_list})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "cc618503",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73.39447410000024"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_sample_means= estimate_df['estimate'].mean()\n",
    "mean_sample_means #73.4%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "72ee2a28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<Axes: title={'center': 'estimate'}>]], dtype=object)"
      ]
     },
     "execution_count": 22,
     "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": [
    "# distribution of the estimate_df:\n",
    "estimate_df.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a527a78a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " # Generate a grid of 100 values from xmin to xmax.\n",
    "\n",
    " ### YOUE CODE HERE ###\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.hist(estimate_df['estimate'], bins=25, density=True, alpha=0.5, label = \"histogram of sample means of 10000 random samples\")\n",
    "xmin, xmax = plt.xlim()\n",
    "x = np.linspace(xmin, xmax, 100) # generate a grid of 100 values from xmin to xmax.\n",
    "p = stats.norm.pdf(x, estimate1, df_std)\n",
    "\n",
    "\n",
    "plt.axvline(x=df_mean, color='m', linestyle = 'solid', label = 'population mean')\n",
    "plt.axvline(x=estimate1, color='r', linestyle = '--', label = 'sample mean of the first random sample')\n",
    "plt.axvline(x=mean_sample_means, color='b', linestyle = ':', label = 'mean of sample means of 10000 random samples')\n",
    "plt.title(\"Sampling distribution of sample mean\")\n",
    "plt.xlabel('sample mean')\n",
    "plt.ylabel('density')\n",
    "plt.legend(bbox_to_anchor=(1.04,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5aad7ca",
   "metadata": {},
   "source": [
    "#### Summary:\n",
    "- The first sample of 50 districts estimated the mean district literacy rate is 74.22 percent, which is relatively close to the population mean of 73.4 percent.\n",
    "\n",
    "- To ensure your estimate will be useful to the government, you can compare the nation's literacy rate to other benchmarks, such as the global literacy rate or the literacy rate of peer nations. If the nation's literacy rate is below these benchmarks, this may help convince the government to devote more resources to improving literacy across the country.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d0a68aa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47b8c21f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}