issues6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "41ab2522",
   "metadata": {},
   "outputs": [],
   "source": [
    "# EXERCISE_1\n",
    "# 1.Explain the difference between median and middle value?\n",
    "#   The median is a measure of central tendency that represents the middle value of a dataset when it is ordered from smallest to largest. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values.\n",
    "#   The middle value is simply the value that occupies the middle position in a dataset. It does not necessarily have to be the median. For example, in the dataset [1, 3, 5, 7, 9], the median is 5, while the middle value is also 5 because it occupies the middle position. However, in the dataset [1, 2, 3, 4, 5, 6], the median is (3 + 4) / 2 = 3.5, but the middle value is 4.\n",
    "\n",
    "# 2.Are mean and mode values always the same for unsorted and sorted dataset? Why?\n",
    "#   The mean (average) and mode (most frequent value) may or may not be the same for unsorted and sorted datasets.\n",
    "#   For the mean, sorting the dataset does not change the sum of the values, so the mean remains the same whether the dataset is sorted or not.\n",
    "#   For the mode, sorting the dataset may change the frequency distribution of the values, potentially affecting which value appears most frequently and thus changing the mode. However, if there is a single mode (one value that appears most frequently), it will remain the same regardless of sorting.\n",
    "\n",
    "# 3.If range is caculate with last datapoint – first datapoint, should the dataset is sorted first or not? Why?\n",
    "#   It doesn't matter whether the dataset is sorted or not when calculating the range. The range is simply the difference between the maximum and minimum values in the dataset.\n",
    "#   Sorting the dataset does not change the maximum and minimum values, so whether the dataset is sorted or not, the range will be the same.\n",
    "#   Therefore, sorting the dataset is unnecessary and does not affect the calculation of the range.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8959edfb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[55, 30, 39, 45, 39, 37, 69, 23, 42, 30, 52, 60, 50, 34, 64, 61, 36, 70, 52, 62, 65, 31, 69, 48, 33, 64, 56, 40, 51, 40, 70, 37, 29, 65, 22, 43, 68, 56, 67, 49, 54, 59, 53, 26, 31, 30, 65, 54, 22, 31, 39, 56, 43, 32, 60, 36, 51, 63, 20, 70, 51, 29, 40, 29, 42, 61, 26, 27, 28, 68, 57, 45, 54, 61, 58, 59, 36, 61, 51, 46, 54, 46, 44, 42, 52, 60, 26, 29, 38, 47, 24, 67, 42, 67, 59, 31, 31, 56, 53, 28]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_2\n",
    "import random as rnd\n",
    "x = [\n",
    "    rnd.randint(20, 70)\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='pink', edgecolor='green')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Histogram of Random Data by izanor the king of coding')\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": 7,
   "id": "a01ca7c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_3\n",
    "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": 8,
   "id": "9f4f438c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_4\n",
    "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": 11,
   "id": "87aab78d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#EXERCISE_5\n",
    "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='w')\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='w')\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='w')\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='w')\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='w')\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='w')\n",
    "plt.xlim([60,340])\n",
    "plt.title(\"si = 20\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "041140c7",
   "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
}