lesson_4_locating_percentiles.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aba7491a-8d04-4477-88d8-da2e4b4c9c7b",
   "metadata": {},
   "source": [
    "# Measures of Position\n",
    "- Methods of describing spread of data include determining the location of values that divide a set of observations into equals parts\n",
    "- These measures include quartiles, deciles, and percentiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f4c330bb-d2bf-40de-b81c-a351265b20dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c9fb973c-5e25-4bf5-99d4-c241f2387642",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = 'data/hotel_bookings.csv'\n",
    "df = pd.read_csv(data_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "f3bf8e53-bf6e-427d-b1e5-1bb50c3df45c",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "adr_sample = df.sample(152).adr.values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a51f138-c92a-4408-aeb2-2320b4f06d9f",
   "metadata": {},
   "source": [
    "## 1. Percentile Computation\n",
    "- $L_p$ refers to the location of adesired percentile\n",
    "- $L_p = (n+1)\\frac{P}{100}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "a1dbfcd2-878d-4f79-88ec-57d0e4baa9ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 1: Organize the data from lowest to largest value\n",
    "orderd_adr_sample = sorted(adr_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "c71a7e3e-a3a9-4caf-a700-fca0b15e24fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(38.25, 114.75)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 2: Computer the first and third quartiles.\n",
    "len_adr_sample = len(adr_sample)\n",
    "L_25 = (len_adr_sample + 1)*(25/100)\n",
    "L_75 = (len_adr_sample + 1) * (75/100)\n",
    "L_25, L_75 # Notice this is position (index), not value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "2ea9bfb5-0b10-484c-813c-23afe90a852a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(68.34, 67.86)"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_index = int(L_25)\n",
    "V_25 = orderd_adr_sample[base_index] + (L_25%1)*(orderd_adr_sample[base_index+1]-orderd_adr_sample[base_index])\n",
    "V_25, np.percentile(orderd_adr_sample, 25)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7ad35d6-e36d-4fed-8287-a26e2b0afcda",
   "metadata": {},
   "source": [
    "# Skewness\n",
    "1. There are 4 shapes commonly observed:\n",
    "   - Symmetric\n",
    "   - Positively Skewed\n",
    "   - Negatively Skewed\n",
    "   - Bimodal\n",
    "2. The coefficient of skewness can range from -3 upto 3.\n",
    "   - A value near -3, indicates considerable negative skewness.\n",
    "   - A value such as 1.63 indicates moderate positive skewness\n",
    "   - A value of 0, occur when the mean and median are equal => the distribution is symmetrical\n",
    "3. Pearson's coefficient of skewness\n",
    "   - $sk = \\frac{3(\\bar{X}-Median)}{std}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "9290a629-8bec-4741-9688-c3449c01c13b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "efe3f81e-50bd-42a2-b8be-fe92e16b2399",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "sns.histplot(adr_sample, bins=8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "da62146a-6c2f-468b-8323-e9aef31ced61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5361794647446517"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "skewness = 3*(np.mean(adr_sample)-np.median(adr_sample))/np.std(adr_sample)\n",
    "skewness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "60804486-b8b3-4e7e-992e-18262c4d812e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6958453198919285"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.skew(adr_sample) # different calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c468121-553d-4677-a567-77aa11303816",
   "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": "3.8.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}