histogram.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0b709e83-4808-449a-9b85-919ab1121224",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "20d73197-8219-4b27-941a-ad19ab18c122",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F(x)={\n",
      "0.1111 for 22.0 <= x < 25.8\n",
      "0.0556 for 25.8 <= x < 29.6\n",
      "0.1667 for 29.6 <= x < 33.4\n",
      "0.1111 for 33.4 <= x < 37.2\n",
      "0.1111 for 37.2 <= x < 41.0\n",
      "0.0556 for 41.0 <= x < 44.8\n",
      "0.1111 for 44.8 <= x < 48.599999999999994\n",
      "0.1111 for 48.599999999999994 <= x < 52.4\n",
      "0.0556 for 52.4 <= x < 56.199999999999996\n",
      "0.1111 for 56.199999999999996 <= x < 60.0\n",
      "}\n",
      "Density at point 21.26: 0\n"
     ]
    }
   ],
   "source": [
    "def plot_histogram(data, point):\n",
    "    hist, bin_edges = np.histogram(data, bins=10, density=True)\n",
    "    plt.hist(data, bins=5, density=True, alpha=0.6, color='b', edgecolor='#000000')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Probability Density')\n",
    "    plt.title('Histogram')\n",
    "    plt.show()\n",
    "\n",
    "    bin_centers = (bin_edges[1:] + bin_edges[:-1]) / 2\n",
    "    pdf_values = hist * np.diff(bin_edges)\n",
    "\n",
    "    print('F(x)={')\n",
    "    for i in range(len(bin_edges) - 1):\n",
    "        print(f'{pdf_values[i]:.4f} for {bin_edges[i]} <= x < {bin_edges[i+1]}')\n",
    "    print('}')\n",
    "\n",
    "    # Calculate density at the given point\n",
    "    density = 0\n",
    "    for i in range(len(bin_edges) - 1):\n",
    "        if bin_edges[i] <= point < bin_edges[i+1]:\n",
    "            density = pdf_values[i]\n",
    "            break\n",
    "\n",
    "    print(f\"Density at point {point}: {density}\")\n",
    "    \n",
    "data = [22, 25, 28, 30, 32,33,35,35,38,40,42,45,47,50,52,55,58,60]\n",
    "point = 21.26  # Example point\n",
    "plot_histogram(data, point)"
   ]
  }
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