distribution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ee26d84a-84c1-4213-bff5-b292e6209530",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average: 5.789670882644963e+76\n",
      "Minimum: 2.5864094916306364e+70\n",
      "Maximum: 1.1579206338612535e+77\n",
      "Standard Deviation: 3.3430160251413314e+76\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import csv\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "file_path = 'integers.csv'\n",
    "values = []\n",
    "with open(file_path, newline='') as csvfile:\n",
    "    csvreader = csv.reader(csvfile, delimiter=',')\n",
    "    next(csvreader, None)\n",
    "    for row in csvreader:\n",
    "        try:\n",
    "            value = float(row[1])\n",
    "            if np.isfinite(value):\n",
    "                values.append(value)\n",
    "            else:\n",
    "                print(f\"Non-finite number found and skipped: {row[1]}\")\n",
    "        except ValueError as e:\n",
    "            print(f\"Error converting '{row[1]}' to float: {e}\")\n",
    "\n",
    "if not values:\n",
    "    raise ValueError(\"No valid numeric data found in the file.\")\n",
    "\n",
    "data = np.array(values)\n",
    "average = np.mean(data)\n",
    "minimum = np.min(data)\n",
    "maximum = np.max(data)\n",
    "std_dev = np.std(data)\n",
    "print(f\"Average: {average}\")\n",
    "print(f\"Minimum: {minimum}\")\n",
    "print(f\"Maximum: {maximum}\")\n",
    "print(f\"Standard Deviation: {std_dev}\")\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.hist(data, bins=50, color='blue', alpha=0.7, density=True)\n",
    "plt.title('Probability Distribution of Values')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.grid(True)\n",
    "plt.axvline(average, color='red', linestyle='dashed', linewidth=2)\n",
    "plt.text(average, plt.ylim()[1]*0.9, f'Mean: {average:.2f}', color = 'red')\n",
    "plt.show()\n"
   ]
  }
 ],
 "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}