{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_list_odd  = [6, 20, 15, 13, 2, 6, 8]      # sorted [2, 6, 6, 8, 13, 15, 20]\n",
    "x_list_even = [6, 20, 15, 13, 2, 6, 8, 25]  # sorted [2, 6, 6, 8, 13, 15, 20, 25]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function to explicitly compute the median from its definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_median(values):\n",
    "    \"\"\"\n",
    "    Compute the median of a list of values.\n",
    "    @param values the list of values.\n",
    "    @return the median.\n",
    "    \"\"\"\n",
    "    \n",
    "    count = len(values)             # count of values     \n",
    "    middle_index = count//2         # index of the middle value when count is odd\n",
    "    sorted_values = sorted(values)  # must work with sorted values\n",
    "    \n",
    "    if count%2 == 1:  # odd number of values\n",
    "        median_value = sorted_values[middle_index]\n",
    "    else:             # even number of values\n",
    "        low_median_value  = sorted_values[middle_index - 1]\n",
    "        high_median_value = sorted_values[middle_index]\n",
    "        median_value = (low_median_value + high_median_value)/2\n",
    "\n",
    "    return median_value "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_median_odd  = my_median(x_list_odd)\n",
    "my_median_even = my_median(x_list_even)\n",
    "  \n",
    "print(f'my_median(x_list_odd)  = {my_median_odd:5.2f}')\n",
    "print(f'my_median(x_list_even) = {my_median_even:5.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## statistics.median function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statistics\n",
    "\n",
    "median_list_odd  = statistics.median(x_list_odd)\n",
    "median_list_even = statistics.median(x_list_even)\n",
    "\n",
    "print(f'statistics.median(x_list_odd)  = {median_list_odd:5.2f}')\n",
    "print(f'statistics.median(x_list_even) = {median_list_even:5.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create NumPy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x_array_odd  = np.array(x_list_odd)\n",
    "x_array_even = np.array(x_list_even)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## np.median function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np_median_list_odd   = np.median(x_list_odd)    # operate on an odd-numbered list\n",
    "np_median_list_even  = np.median(x_list_even)   # operate on an even-numbered list\n",
    "np_median_array_odd  = np.median(x_array_odd)   # operate on an odd-numbered array\n",
    "np_median_array_even = np.median(x_array_even)  # operate on an even-numbered array\n",
    "\n",
    "print(f'np.median(x_list_odd)   = {np_median_list_odd:5.2f}')\n",
    "print(f'np.median(x_list_even)  = {np_median_list_even:5.2f}')\n",
    "print(f'np.median(x_array_odd)  = {np_median_array_odd:5.2f}')\n",
    "print(f'np.median(x_array_even) = {np_median_array_even:5.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-d array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix = np.array([[2, 5, 6, 3],\n",
    "                   [1, 7, 0, 4],\n",
    "                   [3, 1, 2, 6]])\n",
    "\n",
    "median_of_all  = np.median(matrix)\n",
    "median_of_cols = np.median(matrix, axis=0)\n",
    "median_of_rows = np.median(matrix, axis=1)\n",
    "\n",
    "print(f'np.median(matrix) [all]          = {median_of_all}')\n",
    "print(f'np.median(matrix, axis=0) [cols] = {median_of_cols}')\n",
    "print(f'np.median(matrix, axis=1) [rows] = {median_of_rows}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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