lab-sessions-26a/session-2-intuition/main.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "799ee5dc",
   "metadata": {},
   "source": [
    "# Week 2 lab: Descriptive stattistics + Bootstrap(sampling variability)\n",
    "\n",
    "Keypoints:\n",
    "- Descriptive statistics (center, spread, shape)\n",
    "- population vs sample\n",
    "- sampling variability\n",
    "\n",
    "Lab focus: \n",
    "- Bootstrap intuition (mean vs median)\n",
    "- Why estimates \"move\"\n",
    "- effect of sample size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3cd42504",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00123015,  0.29874554, -0.27413786])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# cell 1: Imports + settings\n",
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "rng = np.random.default_rng(7) \n",
    "rng.normal(size=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dee5625",
   "metadata": {},
   "source": [
    "# Example 1: Descriptive statistic\n",
    "We will compute the mean, median, SD, variance, IQR, five-number summary, and flag out the outliers using the $1.5\\times IQR$ rule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7e5313f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0    2.720289\n",
       " 1    3.251926\n",
       " 2    2.306007\n",
       " 3    1.593041\n",
       " 4    2.069273\n",
       " Name: x, dtype: float64,\n",
       " count    60.000000\n",
       " mean      3.025476\n",
       " std       2.512343\n",
       " min       0.600462\n",
       " 25%       1.674114\n",
       " 50%       2.626124\n",
       " 75%       3.280787\n",
       " max      18.123107\n",
       " Name: x, dtype: float64)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 2: Build a dataset with skew + outlier\n",
    "rng = np.random.default_rng(7) \n",
    "n = 60 \n",
    "x = rng.lognormal(mean=1.0, sigma=0.6, size=n) #right-skew\n",
    "x[-1] *= 10\n",
    "x = pd.Series(x, name=\"x\")\n",
    "x.head(), x.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "34a14a88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'min': np.float64(0.6004620561861885),\n",
       "  'Q1': np.float64(1.6741136607158649),\n",
       "  'median': np.float64(2.6261243464658732),\n",
       "  'Q3': np.float64(3.2807868747809836),\n",
       "  'max': np.float64(18.12310679128717)},\n",
       " np.float64(1.6066732140651188),\n",
       " np.float64(-0.7358961603818135),\n",
       " np.float64(5.690796695878662))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cell 3: Five-numbers + IQR + outliers fence:\n",
    "q1 = x.quantile(0.25)\n",
    "q2 = x.quantile(0.50)\n",
    "q3 = x.quantile(0.75)\n",
    "iqr = q3-q1\n",
    "\n",
    "lowerFence = q1-1.5*iqr\n",
    "upperFence = q3+1.5*iqr\n",
    "\n",
    "fiveN = {\n",
    "    \"min\": x.min(),\n",
    "    \"Q1\": q1,\n",
    "    \"median\": x.median(),\n",
    "    \"Q3\": q3,\n",
    "    \"max\": x.max()\n",
    "}\n",
    "fiveN, iqr, lowerFence, upperFence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "1886a0a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'mean': np.float64(3.0254764501575737),\n",
       "  'median': np.float64(2.6261243464658732),\n",
       "  'std': np.float64(2.512343173247777),\n",
       "  'var': np.float64(6.31186822016471),\n",
       "  'IQR': np.float64(1.6066732140651188),\n",
       "  'nOutliers': 5},\n",
       " 7      6.074679\n",
       " 44     6.142882\n",
       " 49     9.027269\n",
       " 58     6.443769\n",
       " 59    18.123107\n",
       " Name: x, dtype: float64)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outliers = x[(x<lowerFence) | (x>upperFence)]\n",
    "summary = {\n",
    "    \"mean\": x.mean(),\n",
    "    \"median\": x.median(),\n",
    "    \"std\": x.std(ddof=1),\n",
    "    \"var\": x.var(ddof=1),\n",
    "    \"IQR\": iqr,\n",
    "    \"nOutliers\": len(outliers)\n",
    "}\n",
    "summary, outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "af45b496",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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L28jlANWsTRVupyvcYvHRRx+liRMnNj2fPHlyeu6559J6662XNt988+jvxxJ8uuDT9M7H76QiLfnS0jw+T59XzFN+izj88MPTbbfdls4888wyeOVWifyo+OCDD8rpeb7crJjnyx2fKnLyr0xvtPJq5HKAanZ4lW2nKxws/vGPf5Q33qio9J8YMmRIGjFiROy3Y4natWmX/nzYn9N/5/x3qSW0Xof10pTXpijBJcgb2aBBg5Z7583m863pO9mtScoBqt/hVbS/WuFgkS9X0cS+5m289sblY1mmJMFiafLG9lkuvfqs89U75QDVr02V7K/0sQAAwggWAEAYwQIACCNYAABhBAsAIIxgAQAIFgBA9dFiAQCEqZtgsc0226Rx48aVQ+qDOgWoPav9101bSqdOnWr6FzxZnDoFqD1102IBAKx5ggUAEEawAADCCBYAQBjBAgAII1gAAGEECwAgjGABAIQRLACAMIIFABCmbm7p3dJmzZpVDsePH79a3r/jh6+nPimlCa++mma/s2Cl3mPChAnh3wsAlkWwWEmvvvpqOTzppJPS6rDxOq3Sybu0S9f94tj0zkfFKr1X586dw74XACyLYLGSBg8e3PQLnPnHslaXgav4+hwqevXqFfRtAGDZWhVFsWp/Dq+gGTNmpK5du6bp06enLl26tORHAwCr+fit8yYAEEawAADCCBYAQBjBAgAII1gAAGEECwAgjGABAIQRLACAMIIFABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAMIIFgBAGMECAAgjWAAAYQQLACCMYAEAhBEsAIAwggUAEEawAADCCBYAQBjBAgAQLACA6qPFAgAII1gAAGEECwAgjGABAIQRLACAMIIFABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAMIIFgBAGMECAAgjWAAAYQQLACCMYAEAhBEsAIAwggUAEEawAADCCBYAQBjBAgAII1gAAGEECwAgjGABAIQRLACAMIIFABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAMIIFgBAGMECAAgjWAAAYQQLACCMYAEAhBEsAADBAgCoPlosAIAwggUAEEawAADCCBYAQBjBAgAII1gAAGEECwAgjGABAIQRLACAMIIFABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAMIIFgBAGMECAAgjWAAAYQQLACCMYAEAhBEsAIAwggUAEEawAADCCBYAQBjBAgAII1gAAGEECwAgjGABAIQRLACAMIIFABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAMIIFgBAGMECABAsAIDqo8UCAAgjWAAAYQQLACCMYAEAhBEsAIAwggUAEEawAADCCBYAQBjBAgAII1gAAGEECwAgjGABAIQRLACAMIIFABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAMIIFgBAGMECAAgjWAAAYQQLACCMYAEAhBEsAIAwggUAEEawAADCCBYAQJi2qYUVRVEOZ8yY0dIfDQCspMpxu3Icr5pgMXPmzHK42WabtfRHAwABx/GuXbsudXqrYnnRI9iCBQvSlClTUufOnVOrVq0WS0M5cLz99tupS5cuqdFY/sau/8w60NjrQKPXf9boZTCjipc/x4UcKrp3755at25dPS0W+ctsuummy5wnF2a1FWhLsvyNXf+ZdaCx14FGr/+s0cugS5Uu/7JaKip03gQAwggWAEB9Bov27dunYcOGlcNGZPkbu/4z60BjrwONXv9Zo5dB+zpY/hbvvAkA1K+qarEAAGqbYAEAhBEsAIAwggUAULvB4pprrkk9evRIHTp0SHvssUd6+umnlzn/rbfemrbZZpty/u233z6NGjUq1aJLL7007bbbbuUdRzfccMM0ePDg9Nprry3zNSNGjCjvTtr8kcuhFl144YWLLUuu10ao+4q83i9aBvkxdOjQuqz/sWPHpgEDBpR36cvf/c4771xoeu43fsEFF6Ru3bqljh07pgMPPDC98cYb4fuQai2DTz/9NJ1zzjnlur322muX83zjG98o70wcvS1V6zpw/PHHL7YsBx98cN2sA2OXs/xL2h/kxxVXXFHT9d+iweIvf/lLOuOMM8pLacaPH5/69u2bDjrooPTee+8tcf7HH388HXPMMemEE05Izz77bHkwzo+XXnop1ZpHHnmkPIA8+eST6cEHHyx3Kv369Usff/zxMl+X77w2derUpsdbb72VatW222670LI89thjS523nuq+4plnnllo+fN6kB155JF1Wf953c7beD4ILMnll1+efv3rX6ff/e536amnnioPrnl/MGfOnLB9SDWXwaxZs8plOP/888vh7bffXv6xMXDgwNBtqZrXgSwHiebLcvPNNy/zPWtpHfh4OcvffLnz44YbbiiDwle+8pXarv+iBe2+++7F0KFDm57Pnz+/6N69e3HppZcucf6jjjqq6N+//0Lj9thjj+Lkk08uat17772XL/MtHnnkkaXOM3z48KJr165FPRg2bFjRt2/fzzx/Pdd9xQ9+8INiq622KhYsWFD39Z/X9TvuuKPpeV7mjTfeuLjiiiuaxn344YdF+/bti5tvvjlsH1LNZbAkTz/9dDnfW2+9FbYtVfPyDxkypBg0aNAKvU+trgPpM9R/Lov9999/mfPUQv23WIvF3Llz07hx48rmzua/G5KfP/HEE0t8TR7ffP4sJ9OlzV9Lpk+fXg7XW2+9Zc730UcfpS222KL8UZpBgwall19+OdWq3MydmwS33HLL9LWvfS3961//Wuq89Vz3le1h5MiR6Vvf+tZiP8ZXr/Xf3OTJk9M777yzUB3n3yDIzdpLq+OV2YfU4n4hrw/rrrtu2LZU7caMGVOeHt56663TKaeckj744IOlzlvP68C7776b7r333rKVdnmqvf5bLFi8//77af78+WmjjTZaaHx+nncwS5LHr8j8tSL/wutpp52W9tprr7Tddtstdb68oeWmsbvuuqs8COXX7bnnnunf//53qjX5gJH7DNx///3p2muvLQ8se++9d/lLeY1U9xX5XOuHH35YnmNuhPpfVKUeV6SOV2YfUkvyKaDc5yKfAlzWj0+t6LZUzfJpkD/+8Y/poYceSpdddll5yviQQw4p67nR1oEbb7yx7IN3+OGHL3O+Wqj/Fv91U1LZ1yL3FVjeebEvfvGL5aMiH1T69OmTrrvuuvSzn/2spooy7ywqdthhh3LjyH+J33LLLZ8podebP/zhD2WZ5L86GqH+Wbbc5+qoo44qO7Tmg0WjbEtHH3100/9zJ9a8PFtttVXZinHAAQekRnLDDTeUrQ/L66BdC/XfYi0W66+/fmrTpk3Z3NNcfr7xxhsv8TV5/IrMXwtOPfXUdM8996SHH354uT8fv6i11lor7bTTTmnixImp1uWm3t69ey91Weqx7ityB8zRo0enE088sWHrv1KPK1LHK7MPqaVQkdeL3KF3RX8qe3nbUi3JTfu5npe2LPW6Djz66KNlx90V3SdUa/23WLBo165d2mWXXcomr4rctJufN/+rrLk8vvn8Wd7wljZ/Nct/ieRQcccdd6S//e1vqWfPniv8HrkJ8MUXXywvz6t1ue/ApEmTlros9VT3ixo+fHh5Trl///4NW/95/c8HguZ1PGPGjPLqkKXV8crsQ2olVORz5jlsfu5znwvflmpJPs2X+1gsbVnqcR2otGDm5cpXkNRF/bdkT9E///nPZa/vESNGFK+88krx7W9/u1h33XWLd955p5z+9a9/vTj33HOb5v/73/9etG3btrjyyiuLCRMmlL1h11prreLFF18sas0pp5xS9vAfM2ZMMXXq1KbHrFmzmuZZdPkvuuii4oEHHigmTZpUjBs3rjj66KOLDh06FC+//HJRa84888xy2SdPnlzW64EHHlisv/765dUx9V73zeUe7JtvvnlxzjnnLDat3up/5syZxbPPPls+8q7mqquuKv9fueLh5z//ebn933XXXcULL7xQ9ojv2bNnMXv27Kb3yD3kf/Ob33zmfUgtlcHcuXOLgQMHFptuumnx3HPPLbRf+OSTT5ZaBsvblmpl+fO0H/7wh8UTTzxRLsvo0aOLnXfeuejVq1cxZ86culgHZi5nG8imT59edOrUqbj22muX+B61WP8tGiyyXEB5x9quXbvysqEnn3yyadq+++5bXn7U3C233FL07t27nH/bbbct7r333qIW5ZVqSY98SeHSlv+0005rKquNNtqoOPTQQ4vx48cXteirX/1q0a1bt3JZNtlkk/L5xIkTG6Lum8tBIdf7a6+9tti0eqv/hx9+eInrfGUZ8yWn559/frls+UBxwAEHLFYuW2yxRRkqP+s+pJbKIB8YlrZfyK9bWhksb1uqleXPf1T169ev2GCDDco/GvJynnTSSYsFhFpeBx5ezjaQXXfddUXHjh3Ly62XpBbr38+mAwBh/FYIABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAMIIFsAqmTZtWvlLpZdccknTuMcff7z8JcpFf6EWqH9+KwRYZaNGjUqDBw8uA8XWW2+ddtxxxzRo0KB01VVXKV1oMIIFEGLo0KFp9OjRadddd00vvvhieuaZZ1L79u2VLjQYwQIIMXv27LTddtult99+O40bNy5tv/32ShYakD4WQIhJkyalKVOmpAULFqQ333xTqUKD0mIBrLK5c+em3XffvexbkftYXH311eXpkA033FDpQoMRLIBVdtZZZ6XbbrstPf/882mdddZJ++67b+ratWu65557lC40GKdCgFUyZsyYsoXipptuSl26dEmtW7cu///oo4+ma6+9VulCg9FiAQCE0WIBAIQRLACAMIIFABBGsAAAwggWAEAYwQIACCNYAABhBAsAIIxgAQCEESwAgDCCBQAQRrAAAFKU/wcC8CzD3rZu0AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cell 5: Visual Diagnostics - boxplot + histogram\n",
    "nBins = 25\n",
    "plt.figure()\n",
    "plt.hist(x, bins=nBins)\n",
    "plt.title(\"Histogram\")\n",
    "plt.xlabel(\"x\"); plt.ylabel(\"Counts\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure()\n",
    "plt.boxplot(x, vert=False, showmeans=True)\n",
    "plt.title(\"Boxplot\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv (3.14.2)",
   "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": "3.14.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}