{
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  {
   "cell_type": "markdown",
   "id": "edc4d861-043c-40d2-871f-4489c175939e",
   "metadata": {},
   "source": [
    "# Compute medians in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a85a4659-9b0a-4e38-a3ac-6ad2ba3430d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statistics\n",
    "from math import floor, ceil"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bbd822c-6430-46ba-b79e-9e322f403efb",
   "metadata": {},
   "source": [
    "## Python: Odd-sized list\n",
    "#### First sort the list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4bb47859-9826-4456-af83-222fdb8ba971",
   "metadata": {},
   "outputs": [],
   "source": [
    "original_list_odd = [ 15, 6, 20, 13, 8, 2, 6 ]\n",
    "\n",
    "count = len(original_list_odd)\n",
    "print(f'{count = }')\n",
    "print()\n",
    "\n",
    "print('original list odd:', end='')\n",
    "for i in range(count):\n",
    "    print(f'{original_list_odd[i]:3}', end='')\n",
    "print()\n",
    "\n",
    "sorted_list_odd = sorted(original_list_odd)\n",
    "\n",
    "print('  sorted list odd:', end='')\n",
    "for i in range(count):\n",
    "    print(f'{sorted_list_odd[i]:3}', end='')\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78cfd526-b603-451d-9f1d-d25bd1c45eab",
   "metadata": {},
   "outputs": [],
   "source": [
    "print('row_index  value')\n",
    "\n",
    "for i in range(1, count + 1):\n",
    "    print(f'{i:5d}{sorted_list_odd[i-1]:10d}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2aa9d48-67fe-4690-b461-6c0a57c50141",
   "metadata": {},
   "source": [
    "#### If a list contains an **odd number** of values, the median is the value in the sorted list at the middle row index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "89bc35fd-2cd7-4828-8eb3-ecc226d07a79",
   "metadata": {},
   "outputs": [],
   "source": [
    "middle_index = floor((count + 1)/2)\n",
    "print(f'{middle_index = }')\n",
    "\n",
    "# Subtract 1 because Python list indexes start at 0.\n",
    "median = sorted_list_odd[middle_index - 1]\n",
    "print(f'{median = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "49089d82-993f-4a7c-b6df-9794b58deec9",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f'{statistics.median(original_list_odd) = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c19607b9-ab4f-4abc-930e-d0e8de1581b6",
   "metadata": {},
   "source": [
    "## Python: Even-sized list\n",
    "#### First sort the list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2bc68599-7907-439c-8444-5ea0ebc818c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "original_list_even = original_list_odd + [25,]\n",
    "\n",
    "count = len(original_list_even)\n",
    "print(f'{count = }')\n",
    "print()\n",
    "\n",
    "print('original list even:', end='')\n",
    "for i in range(count):\n",
    "    print(f'{original_list_even[i]:3}', end='')\n",
    "print()\n",
    "\n",
    "sorted_list_even = sorted(original_list_even)\n",
    "\n",
    "print('  sorted list even:', end='')\n",
    "for i in range(count):\n",
    "    print(f'{sorted_list_even[i]:3}', end='')\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "60ba6998-6b92-41c1-a88e-d9d1a95af5a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "print('row_index  value')\n",
    "\n",
    "for i in range(1, count + 1):\n",
    "    print(f'{i:5d}{sorted_list_even[i-1]:10d}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a401f449-3409-4c7e-88e3-2bf13d97cabc",
   "metadata": {},
   "source": [
    "#### If a list contains an **even number** of values, the median is the **average** of the two values in the sorted list at the two middle indexes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08a65ec9-5369-4435-a036-92d1893a967c",
   "metadata": {},
   "outputs": [],
   "source": [
    "middle_index_1 = floor((count + 1)/2)\n",
    "middle_index_2 =  ceil((count + 1)/2)\n",
    "\n",
    "print(f'{middle_index_1 = }')\n",
    "print(f'{middle_index_2 = }')\n",
    "\n",
    "# Subtract 1 because Python list indexes start at 0.\n",
    "median = (sorted_list_even[middle_index_1 - 1] + sorted_list_even[middle_index_2 - 1])/2\n",
    "print(f'{median = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d742093e-1018-4599-bfa4-c76fd0a818e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f'{statistics.median(original_list_even) = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "646e38c8-267d-4576-a02b-bdbe2d6aa73c",
   "metadata": {},
   "source": [
    "## Function to calculate the median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7159ead0-d118-4a2f-888c-2a43183086b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def median_function(lst):\n",
    "    count = len(lst)\n",
    "    middle_index_1 = floor((count + 1)/2)\n",
    "    middle_index_2 =  ceil((count + 1)/2)\n",
    "    \n",
    "    sorted_lst = sorted(lst)\n",
    "    return (sorted_lst[middle_index_1 - 1] + sorted_lst[middle_index_2 - 1])/2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd4b3930-41dd-4a91-aa43-3271781eb24f",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f'{median_function(original_list_even)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c239c14-2a83-49ca-ab54-b115ea0c9971",
   "metadata": {},
   "source": [
    "## Any size list\n",
    "#### Will the function also work for an odd number of values?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a5a52079-e65c-4f48-9173-824a088b2cad",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f'{median_function(original_list_odd)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "271a9e29-952a-4bc3-8f79-feb76cd00be7",
   "metadata": {},
   "source": [
    "#### Yes, if the number of values is odd, indexes `FLOOR((count + 1)/2)` and `CEIL((count + 1)/2)` are equal, and so w'll end up taking the average of two copies of the same median value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "738c376e-0d04-404a-9816-798a947c2c2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "count = 7\n",
    "\n",
    "print(f'{floor((count + 1)/2) = }')\n",
    "print(f'{ ceil((count + 1)/2) = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "66293bd8-a62e-40ca-a834-56ab46e4982f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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