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ngbala6/variance.ipynb

Created May 18, 2021 13:42
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variance.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Measure of Variability - Variance\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Import Packages"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import statistics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sample Data"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"data = {4, 6, 9, 3, 7}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Population Variance"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Variance Calculation using Formula\n",
"\n",
"<img src=\"https://cdn-images-1.medium.com/max/800/1*N_yz5MPvRDBbzRZOTepnzQ.png\" width=\"45000\" height=\"50000\">\n",
"\n",
"By Applying this formula in the code, we will get Population Variance\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.5600000000000005\n"
]
}
],
"source": [
"def variance(data):\n",
" # Number of observations\n",
" n = len(data)\n",
" # Mean of the data\n",
" mean = sum(data) / n\n",
" # Square deviations\n",
" deviations = [(x - mean) ** 2 for x in data]\n",
" # Variance\n",
" variance = sum(deviations) / (n)\n",
" return variance\n",
"\n",
"print(variance(data))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### Population Variance Calculation using Python Packages"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.5600000000000005"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"statistics.pvariance(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sample Variance"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Sample Variance Calculation using Formula\n",
"\n",
"<img src=\"https://cdn-images-1.medium.com/max/800/1*J8_kemaD_2Wb2EOY7YR-1Q.png\" width=\"45000\" height=\"50000\">\n",
"\n",
"By Applying this formula in the code, we will get Sample Variance"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5.7\n"
]
}
],
"source": [
"def variance(data):\n",
" # Number of observations\n",
" n = len(data)\n",
" # Mean of the data\n",
" mean = sum(data) / n\n",
" # Square deviations\n",
" deviations = [(x - mean) ** 2 for x in data]\n",
" # Variance\n",
" variance = sum(deviations) / (n - 1)\n",
" return variance\n",
"\n",
"print(variance(data))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Sample Variance Calculation using Statistics Python Package"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.7"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"statistics.variance(data)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 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": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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