Issue6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bd1b5231",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1. The median serves as a central tendency measure, indicating the middle value of a dataset when arranged from lowest to highest. If the dataset has an odd number of elements, the median is the value at the center. In cases of an even number, it's the average of the two middle values. The middle value is merely the value at the center of the dataset and may not always coincide with the median. For instance, in [1, 3, 5, 7, 9], the median is 5, aligning with the middle value. Yet, in [1, 2, 3, 4, 5, 6], the median is 3.5, while the middle value is 4.\n",
    "\n",
    "# 2. The mean (average) and mode (most frequent value) may or may not match for unsorted and sorted datasets. Sorting doesn't affect the sum of values, hence the mean remains consistent regardless of sorting. However, sorting may alter the frequency distribution, impacting which value appears most frequently and thus influencing the mode. Yet, if there's a single mode, it will persist irrespective of sorting.\n",
    "\n",
    "# 3. Sorting isn't pertinent in determining the range, which is the difference between the maximum and minimum values in the dataset. As sorting doesn't change these extreme values, whether the dataset is sorted or not, the range remains unaffected. Thus, sorting is unnecessary and doesn't alter range calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6da9666f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[69, 49, 55, 38, 46, 73, 21, 12, 20, 77, 52, 42, 20, 67, 18, 13, 44, 14, 79, 29, 80, 29, 44, 33, 11, 40, 48, 67, 70, 48, 79, 68, 58, 27, 16, 41, 28, 73, 77, 16, 47, 37, 17, 67, 44, 25, 55, 33, 52, 74, 62, 74, 37, 22, 28, 72, 78, 43, 52, 59, 79, 70, 41, 10, 40, 69, 29, 62, 16, 22, 12, 63, 51, 33, 26, 70, 13, 70, 39, 10, 48, 37, 29, 22, 48, 38, 17, 64, 29, 61, 60, 73, 28, 17, 27, 27, 69, 64, 76, 19]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random as rnd\n",
    "x = [\n",
    "    rnd.randint(10, 80)\n",
    "    for i in range(0, 100)\n",
    "]\n",
    "print(x)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(x, bins=25, color='olive', edgecolor='blue')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Rasha data in Histogram')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# In this example, I've chosen bins=25 to divide the data into 25 equally spaced bins.\n",
    "# Because to make the histogram look didn't worst and the detailed information is easy to read.\n",
    "# You can adjust the number of bins based on your preference and the distribution of your data.\n",
    "# If you have more data points or if you want more detailed information about the distribution, you may consider increasing the number of bins.\n",
    "# Conversely, if you have fewer data points or if you want a broader overview of the distribution, you may consider decreasing the number of bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7442e511",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import statistics as stat\n",
    "N = 1000; a = 20; b = 60; x = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    x.append(xi)\n",
    "plt.hist(x, bins=10)\n",
    "plt.xticks(np.arange(20, 64, 4))\n",
    "plt.xlim([20, 60])\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# n = b - a + 1 = 60 - 20 + 1 = 41\n",
    "# Average Value = N * 1/n * the width of the bins = 1000 * 1/41 * 4 = 97,5609"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dab7fc29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 6000; a=1; b=6; dice = []\n",
    "for i in range(N):\n",
    "    xi = rnd.randint(a, b)\n",
    "    dice.append(xi)\n",
    "plt.hist(dice, bins=6)\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "# if we choose bin = 6, The value is 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a0051baa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 100\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,1)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 100\")\n",
    "\n",
    "mu = 200\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,4)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 200\")\n",
    "\n",
    "mu = 300\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,7)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"mu = 300\")\n",
    "\n",
    "mu = 100\n",
    "si = 5\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,3)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"si = 5\")\n",
    "\n",
    "mu = 100\n",
    "si = 10\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,6)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"si = 10\")\n",
    "\n",
    "mu = 100\n",
    "si = 20\n",
    "N = 100000\n",
    "values = np.random.normal(mu, si, N)\n",
    "\n",
    "plt.subplot(3,3,9)\n",
    "plt.hist(values, 100)\n",
    "plt.axvline(values.mean(), color='r')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"si = 20\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "60cf649d",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}