lab-sessions-26a/session-5-error/main-live.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2411ab62",
   "metadata": {},
   "source": [
    "# Part A - Repeated measurements\n",
    "- a representative value, using the samples mean \n",
    "- the measurements variability, using the sample standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "79441225",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.98, 5.01, 5.  , 5.03, 4.99, 5.02, 4.97, 5.01])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np \n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "vSamples = np.array([4.98, 5.01, 5.00, 5.03, 4.99, 5.02, 4.97, 5.01])\n",
    "vSamples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f4fb3a51",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean voltage is = 5.0013 V\n",
      "Sample standard deviation is = 0.0203 V\n"
     ]
    }
   ],
   "source": [
    "vMean = vSamples.mean() # np.mean(vSample)\n",
    "vSTD = vSamples.std(ddof=1) #sample standar deviation\n",
    "\n",
    "print(f\"Mean voltage is = {vMean:.4f} V\")\n",
    "print(f\"Sample standard deviation is = {vSTD:.4f} V\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "26b4bdf2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,4))\n",
    "plt.plot(vSamples, 'ok', label=\"Samples\")\n",
    "plt.axhline(vMean, linestyle=\"--\", linewidth=2, label=f\"Mean = {vMean:.4f}\")\n",
    "plt.xlabel(\"Measurements\")\n",
    "plt.ylabel(\"Voltage [V]\")\n",
    "plt.ylim([4.9,5.1])\n",
    "plt.grid(alpha=0.3)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8893bdc0",
   "metadata": {},
   "source": [
    "1. What is the estimated voltage?\n",
    "2. What does the sample standard deviation tell us?\n",
    "3. Are the measurements relatively precise or widely scattered?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3482af0e",
   "metadata": {},
   "source": [
    "# Part B - Propagation of uncertainty of one variable\n",
    "Example area of a cricle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2c2306b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Radius: r = 10.0000 +/- 0.2000 mm\n",
      "Area: A = 314.1593 +/- 12.5664 mm^2\n"
     ]
    }
   ],
   "source": [
    "r = 10.0\n",
    "sigmar = 0.2\n",
    "Area = np.pi*r**2\n",
    "sigmaA = sigmar*(2*np.pi*r)\n",
    "\n",
    "print(f\"Radius: r = {r:.4f} +/- {sigmar:.4f} mm\")\n",
    "print(f\"Area: A = {Area:.4f} +/- {sigmaA:.4f} mm^2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1c60ddad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigmarValues = np.linspace(0.01, 0.5, 10)\n",
    "sigmaAValues = (np.pi*2*r)*sigmarValues\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(sigmarValues, sigmaAValues, 'ok')\n",
    "plt.title(\"Propagation of uncertainty\")\n",
    "plt.xlabel(\"Uncertainty in radius [mm]\")\n",
    "plt.ylabel(\"Uncertainty in area [mm^2]\")\n",
    "plt.grid(alpha=0.3)\n",
    "plt.savefig(\"uncertainty.png\", dpi=300, bbox_inches=\"tight\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56766593",
   "metadata": {},
   "source": [
    "# Part c - Propagation of uncertainty for several variables\n",
    "Example: Resistance from voltage and current.\n",
    "- $V=12.0 \\pm 0.2$\n",
    "- $I=2.0 \\pm 0.05$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "a6583ccf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resistance: R = 6.0000 +/- 0.1803 ohms\n"
     ]
    }
   ],
   "source": [
    "V = 12.0\n",
    "sigmaV = 0.2\n",
    "I = 2.0 \n",
    "sigmaI = 0.05\n",
    "\n",
    "R = V/I\n",
    "sigmaR = np.sqrt((sigmaV/I)**2 + (sigmaI*V/I**2)**2)\n",
    "print(f\"Resistance: R = {R:.4f} +/- {sigmaR:.4f} ohms\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "d57fa95d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Contribution from voltage uncertainty: 30.7692%\n",
      "Contribution from current uncertainty: 69.2308%\n"
     ]
    }
   ],
   "source": [
    "termV = (sigmaV / I)**2\n",
    "termI = ((V * sigmaI) / (I**2))**2\n",
    "total = termV + termI\n",
    "\n",
    "percent_V = 100 * termV / total\n",
    "percent_I = 100 * termI / total\n",
    "\n",
    "print(f\"Contribution from voltage uncertainty: {percent_V:.4f}%\")\n",
    "print(f\"Contribution from current uncertainty: {percent_I:.4f}%\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv (3.14.3)",
   "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": "3.14.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}