heights.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data visualization using `heights` dataset in `dslabs` package\n",
    "\n",
    "In this notebook, data visualization is covered on these two types of data.\n",
    "\n",
    "## Types of data\n",
    "\n",
    "### 1. Categorical\n",
    "    1.a Ordinal data -> can be ordered, eg., spiciness of foods (mild, medium, hot)\n",
    "    1.b Non-ordinal data -> unordered, eg., directions (north, south, east, west)\n",
    "\n",
    "### 2. Numeric\n",
    "    2.a Continues data -> can take precise, decimal values, eg., average score of a student (like 75.128)\n",
    "    2.b Discrete data -> needs to be rounded off to nearest integer, eg., population size of an area\n",
    "\n",
    "## Topics\n",
    "1. Mean, SD, Standard units\n",
    "2. Normal Distributions\n",
    "3. Quantiles\n",
    "4. Percentiles\n",
    "5. Boxplot\n",
    "6. Reordering of vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility functions\n",
    "\n",
    "All the utility functions are defined here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "randomColors = function(numberOfColors = 1) {\n",
    "    cols = c() # empty vector of colors\n",
    "    for (i in 1:numberOfColors) {\n",
    "        r = as.character(as.hexmode(sample(0:255, 1))) # amount of red\n",
    "        if (nchar(r) == 1) r = paste(\"0\", r, sep = \"\")\n",
    "        \n",
    "        g = as.character(as.hexmode(sample(0:255, 1))) # amount of green\n",
    "        if (nchar(g) == 1) r = paste(\"0\", r, sep = \"\")\n",
    "        \n",
    "        b = as.character(as.hexmode(sample(0:255, 1))) # amount of blue\n",
    "        if (nchar(b) == 1) r = paste(\"0\", r, sep = \"\")\n",
    "        \n",
    "        col = paste(\"#\", r,g,b, sep=\"\") # current random color\n",
    "        \n",
    "        if (nchar(col) != 7) col = \"#ff0000\" # safe side\n",
    "        \n",
    "        cols = append(cols, col) # append the current color to the list of colors\n",
    "    }\n",
    "    cols\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "#randomColors(100) # uncomment to test the above function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: 'dplyr'\n",
      "\n",
      "The following objects are masked from 'package:stats':\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "The following objects are masked from 'package:base':\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>sex</th><th scope=col>height</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Male  </td><td>75    </td></tr>\n",
       "\t<tr><td>Male  </td><td>70    </td></tr>\n",
       "\t<tr><td>Male  </td><td>68    </td></tr>\n",
       "\t<tr><td>Male  </td><td>74    </td></tr>\n",
       "\t<tr><td>Male  </td><td>61    </td></tr>\n",
       "\t<tr><td>Female</td><td>65    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " sex & height\\\\\n",
       "\\hline\n",
       "\t Male   & 75    \\\\\n",
       "\t Male   & 70    \\\\\n",
       "\t Male   & 68    \\\\\n",
       "\t Male   & 74    \\\\\n",
       "\t Male   & 61    \\\\\n",
       "\t Female & 65    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "sex | height | \n",
       "|---|---|---|---|---|---|\n",
       "| Male   | 75     | \n",
       "| Male   | 70     | \n",
       "| Male   | 68     | \n",
       "| Male   | 74     | \n",
       "| Male   | 61     | \n",
       "| Female | 65     | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  sex    height\n",
       "1 Male   75    \n",
       "2 Male   70    \n",
       "3 Male   68    \n",
       "4 Male   74    \n",
       "5 Male   61    \n",
       "6 Female 65    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library (dslabs)\n",
    "library (dplyr)\n",
    "data (heights)\n",
    "\n",
    "head (heights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "   Female      Male \n",
       "0.2266667 0.7733333 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Return a table that prints the proportions of height reported for each sex category\n",
    "prop.table(table(heights$sex))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Central Tendencies, Standard Deviation, and Standard Units\n",
    "\n",
    "Report mean, median and max of all heights and summarize them using dplyr's `summarize()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>mean</th><th scope=col>median</th><th scope=col>max</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>68.32301</td><td>68.5    </td><td>82.67717</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " mean & median & max\\\\\n",
       "\\hline\n",
       "\t 68.32301 & 68.5     & 82.67717\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "mean | median | max | \n",
       "|---|\n",
       "| 68.32301 | 68.5     | 82.67717 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  mean     median max     \n",
       "1 68.32301 68.5   82.67717"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "heights %>% summarize(\n",
    "    mean = mean(height),\n",
    "    median = median(height),\n",
    "    max = max(height)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Report the mean and SD for male and female heights separately"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>Mean of male heights</dt>\n",
       "\t\t<dd>69.3147549414356</dd>\n",
       "\t<dt>SD of male heights</dt>\n",
       "\t\t<dd>3.60879945291351</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[Mean of male heights] 69.3147549414356\n",
       "\\item[SD of male heights] 3.60879945291351\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "Mean of male heights\n",
       ":   69.3147549414356SD of male heights\n",
       ":   3.60879945291351\n",
       "\n"
      ],
      "text/plain": [
       "Mean of male heights   SD of male heights \n",
       "           69.314755             3.608799 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the mean, SD, and standard units for male heights\n",
    "indM = heights$sex == \"Male\"\n",
    "male = heights$height [indM]\n",
    "n = length(male)\n",
    "\n",
    "meanM = sum (male) / n\n",
    "sdM = sqrt(sum ( ((male - meanM)^2) / n))\n",
    "zM = (male - meanM) / sdM # standard units\n",
    "\n",
    "c(\"Mean of male heights\" = meanM, \"SD of male heights\" =  sdM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>Mean of female heights</dt>\n",
       "\t\t<dd>64.9394242506451</dd>\n",
       "\t<dt>SD of female heights</dt>\n",
       "\t\t<dd>3.76065612429516</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[Mean of female heights] 64.9394242506451\n",
       "\\item[SD of female heights] 3.76065612429516\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "Mean of female heights\n",
       ":   64.9394242506451SD of female heights\n",
       ":   3.76065612429516\n",
       "\n"
      ],
      "text/plain": [
       "Mean of female heights   SD of female heights \n",
       "             64.939424               3.760656 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the same for female heights, but use the built-in R functions this time\n",
    "indF = heights$sex == \"Female\"\n",
    "female = heights$height [indF]\n",
    "\n",
    "meanF = mean(female)\n",
    "sdF = sd(female)\n",
    "zF = scale(female) # standard units\n",
    "\n",
    "c(\"Mean of female heights\" = meanF, \"SD of female heights\" =  sdF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.949507389162562"
      ],
      "text/latex": [
       "0.949507389162562"
      ],
      "text/markdown": [
       "0.949507389162562"
      ],
      "text/plain": [
       "[1] 0.9495074"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.949579831932773"
      ],
      "text/latex": [
       "0.949579831932773"
      ],
      "text/markdown": [
       "0.949579831932773"
      ],
      "text/plain": [
       "[1] 0.9495798"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the proportions of male and female heights two units away from the SD\n",
    "mean (abs(zM) < 2) \n",
    "mean (abs(zF) < 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normal Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Required proportion:  0.333743842364532'</span>"
      ],
      "text/latex": [
       "'Required proportion:  0.333743842364532'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Required proportion:  0.333743842364532'</span>"
      ],
      "text/plain": [
       "[1] \"Required proportion:  0.333743842364532\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the proportion of male heights more than 69 inches and less than or equal to 72 inches\n",
    "pExact = mean(male > 69 & male <= 72)\n",
    "paste(\"Required proportion: \", pExact)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Approximate proportion:  0.306337940499623'</span>"
      ],
      "text/latex": [
       "'Approximate proportion:  0.306337940499623'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Approximate proportion:  0.306337940499623'</span>"
      ],
      "text/plain": [
       "[1] \"Approximate proportion:  0.306337940499623\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repeat the above computation but using normal distribution\n",
    "# Use: meanM, sdM\n",
    "# Do NOT use: male\n",
    "\n",
    "pApprox = pnorm(72, meanM, sdM) - pnorm(69, meanM, sdM)\n",
    "paste(\"Approximate proportion: \", pApprox)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.08946296962176"
      ],
      "text/latex": [
       "1.08946296962176"
      ],
      "text/markdown": [
       "1.08946296962176"
      ],
      "text/plain": [
       "[1] 1.089463"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Report how many times is the exact proportion larger than the approximate one\n",
    "pExact / pApprox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantiles\n",
    "\n",
    "A **quantile** for a proportion <em>p</em> is defined as the value <em>q</em> such the proportion of values in the data below <em>q</em> is <em>p</em>. <br>\n",
    "\n",
    "    f (x < q) = p\n",
    "\n",
    "Here's an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.514778325123153"
      ],
      "text/latex": [
       "0.514778325123153"
      ],
      "text/markdown": [
       "0.514778325123153"
      ],
      "text/plain": [
       "[1] 0.5147783"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean (male < 69.5) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above cell <br>\n",
    "`x = male`\n",
    "`p ~ 0.51`\n",
    "`q = 69.5`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the quantiles for data (**observed quantiles**) is match the normal quantiles (**theoretical quantiles**), then it means the data is approximated by the normal distribution.\n",
    "\n",
    "The scatter plot between theoretical and observed quantiles is called a **quantile-quantile plot**, or **q-q plot** in short."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"Q-Q plot for males\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define a sequence of values of p\n",
    "p = seq(0, 1, 0.05)\n",
    "\n",
    "# Compute the observed quantile for this sequence for the male heights, using the built-in quantile function\n",
    "qM_obs = quantile(male, p)\n",
    "\n",
    "# Compute the theoretical quantile for the same, using the built-in qnorm function\n",
    "qM_theo = qnorm(p, meanM, sdM)\n",
    "\n",
    "# Check whether they match by drawing a q-q plot them\n",
    "plot (qM_theo, qM_obs, xlab = \"Theoretical quantiles\", ylab = \"Observed quantiles\", main = \"Q-Q plot for males\")\n",
    "abline (0, 1) # draw a line through the plot with intercept = 0 and slope = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I6s8Xk6T7kdQjqSVi+mfVgKKVlZNaS/\nS5x/6BSfv/x9P15TF1q9tJJq/B/LrBjSM2yccDF+tDivqQt1L50/Z9T5igUsQpp7LtLZBLfi\nyLxHEowfCsFL6sDH7SFCElgxpOoA18x9/PJdvKQOlCskrsDghO1bu7g8sW/ChVY7fx2xf7Oj\nC4mjUG0h9Z9ctpHsWR/9XZ1G8f2oVdZIP1b8guIKDE6seGJfdsrFI/+ObaQfKFf0wy8UbwJs\nyU7sm3DJ4qjx3i18iu8VxpSh0Isz9if2ZR8JvdYwUy5Z/HfOP0cK4gufI62JfNxTndjH30fa\nKtZCq+DEPr9R0Uo41s5jrIzWQ0jeoqI1WYeUxNkLFj9E92doFpiPldHKJDsbXj8LpCWxENih\notVZhnQ10TN71a78MebN4CCrX7D+QPbp4gATFoOlir8gkbJSWpvgECFC2ozy+IW0/j9WYhlS\nWK6RuPb371Xv5zgr4hc020hc+9ulSX/sq/6WkH7B+nykSaeOW83i4D6+c27c0L6oSecr1iD5\nHMnEN9HdGZzFsX3c4nnfMHzqOM/hqjiyYeM+rl/KHwydOs5eu/VZhjR6VtFyLARv4yFlO7uH\nRiKjtdnu/o7Ex333Z3FwIyF9PHUc67Pe/W3Mt6s9LsDCUfu0xWPYFNoS222kx+XVUngRv8Vj\n6agNbvFwAMPWCHY2PM6BEb/FY+lo6l/R8fOOBvyIZq/dVfySsnx8Rj2bpFgj5e/upJ8ksah8\nQkUbJdlGCs7a8/oIaRgro+0S7LU7sdduFVS0ZdafI4kPDurPAhlWRhtnGVL8/ZLfS7DQtFHR\n5glO7HOA5aaBldEeCE7sc4Al542K9sH2oNU40u9qIKQKK6PdsH5r5+Rvg7H4ZKhoRwhpo1gZ\n7Qsn9q1mNI3O3xmnor0hpJWMHqvdvpGKdkhyzQau/f3d6NlDjRtZGe2TbUhc+3uajye6tm+k\nor2yDIlrf080JSRWRjtmGRLX/p7oe0gfrmOCfRAcIkRIU4xvIxXvj1e8OxATHCLEtb+nGPt1\nY7j8wu5ptpG49vcEHzaBqoq8fMzHYbvXjmt/26EfT0g+R+La38uwGvIHRzbIzM2CinxCSCIz\n9xewMvKMbUjXME0foQm1ZyXtcCEb3b3dG3iHDxCjLENKskUiyPY2SEva33I2+oFrZ1Ay8pBl\nSJG55Z8h3bS77fa3pE0OiYr8JDiy4W7OHNkwLSRWRt4ShBSbhJCmbCNRkces39rdExOkvLX7\nuteOlZHf7Hc2GHPJFhP+rMtYKlTkO+vd30G2hZRq/xjFPkP6iJXRAfCB7ARWJVDRIRDSVzbn\nOLAyOgrrkG75Qaviv22+qaVv1jELrRGp6DhsQ4rK0yhi1R3qz+LHZhyz0B5vSw8CrlmGdDZB\ntjJKgmzXnc6WlsFFIbEyOhrLkAJzz7/esw+TdLa0FC4IiYqOR3BkQ/sbiU0tiDO3kVgZHZL1\nW7tqjST9032bWhRn7bWjooOyvmZDvo30F0ivD7mtkKavZFgZHZdFSKbtx/fq96joyAhJg5XR\nwXFkgwIVHR4hWWNlBNuQntf8AKGL+k+b72jJpCJkrEJKgnL7KDjoBSJZGaFkE1JizDm7eND9\nbMwRz0eiIrxZhPSsT4t9JSV9d7eDJZSVEZosQjo3jmY4+3vQ6iAqQptFSKGp/27s40h/H4mV\nEXqsPpBt/vAwH8hSEQYcMqTlqxRWRhh2wLd2y6/BQEX45IA7GxZeg4GVEUYcb/f3smswUBFG\n2XwgezPmnJ3Xl30gq72M0MZCYmWEb+wOEXqfQ7Gjy3HNDYmKMIHlQauX7KDVaF8Hrc7aRqIi\nTHLA0yim77VjZYSpDhjS1ECoCNMdMqQp94CMMAchDc7/13cAe0NI/ZmTEWYjpO6sqQgLEFJr\nvmSEZQipMVcqwlKEVM2SjGCBkIoZUhGsEBIrIwgQEhVB4OAhsTKCxqFDoiKo7Csk5QqElRGE\n9hTS8quWfJgWoLKrkFSzZ2UEtR2FtOyqJQPToSLIHS0kVkZw4lghUREc2VFItttIrIzgzq5C\nsthrR0Vwak8hLc+BiuDYvkJaNjEygnPeh0RFWIPfIbEywkp8DomKsBpvQ2JlhDV5GhIVYV0+\nhsTKCKvzLyQqwg94FhIrI/yGVyFREX7Fn5BYGeGHfAmJivBTXoTEygi/5kFIVITf23tIrIyw\nCfsOiYqwETsOiZURtmO3IVERtmSfIbEywsbsMSQqwubsLiRWRtiifYVERdioPYVERdis3YTE\nyghbtpOQqAjbtoeQWBlh87YfEhVhBzYeEisj7MOmQ6Ii7MV2Q2JlhB3ZakhUhF3ZaEhkhH3Z\naEjuZwEoERIgQEiAACEBAoQECBASIEBIgAAhAQJrhvQ8GRMl5URGp0JI2JkVQ3oGJhMXEyEk\n+GTFkM7m+qrpGkT5RAgJPlkxpKAY8RGED0KCZ1YMqWrnGUWEBM+sGFJontV3ESHBLyuGdDWn\n8ruHiQgJXllz9/f5XU/y5fRXQsLOrPqB7D2uvnucBi5d17B4FsBPcGQDIEBIgMAvQvr+zo2Q\nsDOEBAgQEiBASIAAIQEChAQIsPsbECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAA\nAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFC\nAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIE\nCAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJ\nECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAg\nJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRA\ngJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQ\nAAFCAgQICRAgJECAkAABQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRAgJECAkAAB\nQgIECAkQICRAgJAAAUICBAgJECAkQICQAAFCAgQICRD4SUjm2yQICTtDSIDAiiGZNhezAH5k\nxZD+AkKCr9Z8a/eMTfTIp8BbO3hm3W2kmzG3lJDgn5V3NjwiEz8JCd5Zfa/dxQQJIcE36+/+\nvofDexoMsGOrh5SmpyVzncD5eowZbGAO+5/B6jOaa/9P8f5n4MFD2E9IjlZIHjzF+5+BBw+B\nkPb/FO9/Bh48BELa/1O8/xl48BAIaf9P8f5n4MFDIKT9P8X7n4EHD4GQ9v8U738GHjyE/YTk\nyv6f4v3PwIOHQEj7f4r3PwMPHgIh7f8p3v8MPHgIhLT/p3j/M/DgIRASsCeEBAgQEiBASIAA\nIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIDABkO6tu7T4quaT51Beg5M\ncH7qJt+dnvYR9O6t+u47vv85x6/ACstQz/ZCurce8V3/JLRnkEb59EPZ5LvT0z6C3r1V333H\n97+a5Ngc1TNw8Aj6NhfSPeg8CbHbGfyZ4J797E80+d70pI+gN3X13Xd8/4spun0FVliGBmwt\npKuJWk/C1VzczuBskjT7M56q2fSmJ30Evamr777j+19M0O0r4H4ZGrK1kMw57TwJV7cziE32\nJ6V1v7R605M+gt7U1Xff8f3PuH4F3C9DgzN1P4tZ7mn3WU5Ory1RdzMo/yF7B92bnvQR9Kau\nvvuO73/G9SvgfhkasrWQ0t6TkIuczWCFkISP4Cch7ewV6E3MxSPoz9Hp1BfpPMu3NH2epSvn\ndUOSPoIfhLS7V2BgBvpH0J+jy4kvM/CMPqU7R9cNqSB6BD8IqbCjV+DDxLSPoD9HlxOfrrmj\nf+gZtX6WP84gEL2M1Qw+TU+znPSmrrr7n+dQcrecyx/Ch4m5/SDp8CEV+4we1vuMqhl8mp7m\nZexNXXX3P8+h5HITRvwQujMY+Zlwji4nvkzn11V26IjDZ/mSf4qRGNVOnd70pI+gN3X13Xd8\n/0tOX4HeDFw8gv4cXU58mc6nded8QzFxNQPnRzZIH8EPjmzY3SvQm4GLR9Cfo8uJL9N6B/YM\n8rdM0g8B2m/xQvG+0cb0HDyC7tTld9/x/S+4fQW6M3DxCPpzdDr1RdrP8vMcmFC747I/A+Wn\ndY3pOXgEg1OXftjo9v6njQk7ewgrLEP9ObqdPHAMhAQIEBIgQEiAACEBAoQECBASIEBIgAAh\nAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEC\nhAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKE5JppWPKXtZNiIh+nvuAuvSfp9g99HwrPpGuW\nIYWmmMjHqc+/R/UkCUmGZ3IV7b9pumTMZTd/GYeQZHgmV0FIvuOZXEUjpLMJLvn319AE5Z/a\nfn1b/NVtY56hiRs3Fu8Iy/HPgYke2TdJbMq/A95M4XXzpfGOLf9/c8hHnM+6McliwPqOJJEx\nUeLwefAXIa2iDinOFuNssc2/MVH20+j9bX77uXFjM6R8sOCZppdii+uctkLKb760Q2oNGeQD\n9EKq78i1GPq65jPjC0JaRR1S9Hwtr+Hrl3/23TMyr9//NxPc03tgbuXtrRvrKG7ZD09ZFCYb\n9JbfUodUTaUVUmvIatbNm1vzCsw9Gzpc+cnxAiGtog7pr/xXbLJintn7uDhbiLMFurq9eWO9\n1MfZbU8TtKZZh1RNpf3WrjlkNet2SK158bZuKUJaRXtnQ7EMV7vEqxtb33Zu7O6rfiSXqBNS\nbyrF/ztD9ifZmNf59c7yfnf2JHiNkFYhDimqbv0aUnfI0ZDSS7YZFTzcPQ/+IqRVDIXUvbHT\nVPp5jJMJr8ljSki9IYdCat7R5ByyjbQEIa2iH1Jcb49UWzfvLaLmjfUY0XsbKf9ZN6RinL93\nG/V34yHF3Q0jwzKxAE/aKvoh5TvZ0mtWT2uvXT5Y40ZjHuUY12z32rnYa/eX3rvbSEm91y40\n12w/nBkYsvjhI61DaswrLPbxsUZagJBW0Q+p3HrJN0ianyMVw9U3hua9Dnp/jnQut2r+WquP\n/KdRkZzJP5AaGLLorJpk547c3gNjLkJaxUBI2QEF5lRs2F+D95EN5QjvG//Cd0j5XrV8hNOr\nmL/me8FqnDitdhqciu+6Q2b/ryfZvSP5kQ10tAQheYYtnN/gafcMIf0GT7tnCOk3eNo9Q0i/\nwdMOCBASIEBIgAAhAQKEBAgQkltJ8+iD9h616fvXvp5uNzqp8fnkt3ZmEHN+32yE5NQjO/3U\nNqTw64CWIXVn8DSckjQXITkVtS5QsvAznu+jWYQ0OMQ5+jYKOgjJpVt+PYT9hfTMzqfAHITk\nUpj/Zm+H9L52XHlqUFxd5+4cmHNzma4GrM4DH7hEXWus5u3l1fE6k2ydklROwZh6BvVV7SLO\nSZqJkBz6M+1zI97nCuXXjisW6PJic+VpQad6qX8PWC7nQ5eoK8eKe7cXV8erb6zn351vHVLz\nqnZXTkqaiZAcOpv8kjytkOprxxULdH2du/cJroX2gNn/By5R17qYXfv21o31/LvzrU9Lal7V\n7p4HiekIyaEo30Rqh1RfO646Fbx56YSkudQ3B0yb3zfH+uuO9b79w42d+TYv4lDv9X4adjfM\nQ0gOlYtwK6T62nH965A0h+0MmPl4ibryS/did71Jdsdrh9S6qh0Hkc/E8+XQUEj1teO+hNQe\nMB27RF3xpXexu5khta5qR0gz8Xw5VC6NYfn55qO8Pk957bhvIbUGHL1EXf6lf7G7uSE1r2pH\nSDPxfDlUbiOdyr/vcDWn6pbu1snANlJ7wPL/3ZC6F7NrhdS4sZ5YY+B+SO9x2Uaai5AcOhcb\n/UmxT/mWb+HX145rL9C9vXbNAYvr0A1coi5p7rXrXuxuYJL19e6qKRT/PdL2Ve3+2Gs3EyE5\n9GfKD01N/RlPfe24zsomqi/BnasHLK5DN3iJuuKPG53KvRjdi93VNxbq6921Qypm0Lyq3YXP\nkWYiJJfC8g1SdtCBKY+pfl87rhNS/vf4Gu/D6gGL69ANXqIu30NQHrwwcLG7S+dgiff17kCL\nAZQAAABkSURBVNohlTNoXNWOIxvmIiSXktmHUW9j2+TBH0qai5CciiZvauQHJjzjbWybcPT3\nbITk1KPYbzdBeahc8H1I9zgfaT5Ccis5fR+mcH1toYSbWB+lJ97YzUZIgAAhAQKEBAj8AxwY\nbAjtgH0uAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Q-Q plot for females\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repeat the same for female heights, but use standard units instead of mean and SD\n",
    "\n",
    "qF_obs = quantile (zF, p)\n",
    "qF_theo = qnorm (p)\n",
    "plot (qF_theo, qF_obs, \n",
    "      xlab = \"Theoretical quantiles\", \n",
    "      ylab = \"Observed quantiles\", \n",
    "      main = \"Q-Q plot for females\", \n",
    "      sub = \"(Using standard units)\"\n",
    ")\n",
    "abline(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Percentiles\n",
    "\n",
    "A **percentile** referes to a quantile expressed in percent.\n",
    "\n",
    "Refer to the following table as an example.\n",
    "<table>\n",
    "    <thead>\n",
    "        <th> quantile </th>\n",
    "        <th> percentile </th>\n",
    "    </thead>\n",
    "    <tr>\n",
    "        <td> 0.1 </td>\n",
    "        <td> 10 % </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td> 0.25 </td>\n",
    "        <td> 25 % </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td> 0.5 </td>\n",
    "        <td> 50 % </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td> 0.75 </td>\n",
    "        <td> 75 % </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td> 1 </td>\n",
    "        <td> 100 % </td>\n",
    "    </tr>\n",
    "</table>\n",
    "\n",
    "And so on.\n",
    "\n",
    "The middle three rows, namely, 25 %, 50 % and 75 % are called **quartiles**.\n",
    "\n",
    "The middle row, that is the 50th percentile, is called the **median** of the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boxplots\n",
    "\n",
    "For those distributions that do not conform to the normal distribution, boxplots are an effective way of visualizing them.\n",
    "\n",
    "A boxplot is a _five_-number summary that describe data:\n",
    "1. The lower range\n",
    "2. The upper range\n",
    "3. The 25th percentile\n",
    "4. The 50th percentile\n",
    "5. The 75th percentile\n",
    "\n",
    "Thus, **a boxplot is described by a distribution's range, and its quartiles.** \n",
    "\n",
    "The edge percentiles (25%, 75%) are shown in a box, with the median (50%) passing inside it, and the distance between them is called the _inter-qaurtile range_. The range is shown by whiskers outside the box on its Y-axis. \n",
    "\n",
    "Furthermore, we ignore **outliers**, or exceptions, while computing the range, and instead plot them as independent points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw a boxplot for males wrt their heights\n",
    "boxplot(height~sex, data = heights, col=randomColors(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reordering of vectors\n",
    "\n",
    "Using the `reorder()` function that takes the following:\n",
    "\n",
    "• factor variable, <br>\n",
    "• values of each corresponding factor level, <br>\n",
    "• FUNction to reorder the factor, <br>\n",
    "    \n",
    "and returns a new factor reordered as per the function provided in ascending order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'Afiray'</li>\n",
       "\t<li>'Rafi'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Afiray'\n",
       "\\item 'Rafi'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Afiray'\n",
       "2. 'Rafi'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Afiray\" \"Rafi\"  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define a facor with 2 levels\n",
    "fac = factor(c(\"Rafi\", \"Rafi\", \"Afiray\", \"Afiray\"))\n",
    "levels(fac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'Rafi'</li>\n",
       "\t<li>'Afiray'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Rafi'\n",
       "\\item 'Afiray'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Rafi'\n",
       "2. 'Afiray'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Rafi\"   \"Afiray\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "val = c(4, 5, 12, 13) # values for each factor\n",
    "fac = reorder(fac, val, FUN = mean) # reorder the factor levels in order of their means\n",
    "levels(fac)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The notebook ends here."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}