Program for Variance and Standard Deviation of an array
Given an array, we need to calculate the variance and standard deviation of the elements of the array.
Examples :
Input : arr[] = [1, 2, 3, 4, 5]
Output : Variance = 2
Standard Deviation = 1
Input : arr[] = [7, 7, 8, 8, 3]
Output : Variance = 3
Standard Deviation = 1
We have discussed program to find mean of an array.
Mean is average of element.
Mean of arr[0..n-1] = ∑(arr[i]) / n
where 0 <= i < n
Variance is sum of squared differences from the mean divided by number of elements.
Variance = ∑(arr[i] – mean)2 / n
Standard Deviation is square root of variance
Standard Deviation = √(variance)
Please refer Mean, Variance and Standard Deviation for details.
Below is the implementation of above approach:
C++
// CPP program to find variance// and standard deviation of// given array.#include <bits/stdc++.h>using namespace std;// Function for calculating varianceint variance(int a[], int n){ // Compute mean (average of elements) int sum = 0; for (int i = 0; i < n; i++) sum += a[i]; double mean = (double)sum / (double)n; // Compute sum squared // differences with mean. double sqDiff = 0; for (int i = 0; i < n; i++) sqDiff += (a[i] - mean) * (a[i] - mean); return sqDiff / n;}double standardDeviation(int arr[], int n){ return sqrt(variance(arr, n));}// Driver Codeint main(){ int arr[] = {600, 470, 170, 430, 300}; int n = sizeof(arr) / sizeof(arr[0]); cout << "Variance: " << variance(arr, n) << "\n"; cout << "Standard Deviation: " << standardDeviation(arr, n) << "\n"; return 0;} |
Java
// Java program to find variance// and standard deviation of// given array.import java.io.*;class GFG{ // Function for calculating // variance static double variance(double a[], int n) { // Compute mean (average // of elements) double sum = 0; for (int i = 0; i < n; i++) sum += a[i]; double mean = (double)sum / (double)n; // Compute sum squared // differences with mean. double sqDiff = 0; for (int i = 0; i < n; i++) sqDiff += (a[i] - mean) * (a[i] - mean); return (double)sqDiff / n; } static double standardDeviation(double arr[], int n) { return Math.sqrt(variance(arr, n)); } // Driver Code public static void main (String[] args) { double arr[] = {600, 470, 170, 430, 300}; int n = arr.length; System.out.println( "Variance: " + variance(arr, n)); System.out.println ("Standard Deviation: " + standardDeviation(arr, n)); }}// This code is contributed by vt_m. |
Python 3
# Python 3 program to find variance# and standard deviation of# given array.import math# Function for calculating variancedef variance(a, n): # Compute mean (average of # elements) sum = 0 for i in range(0 ,n): sum += a[i] mean = sum /n # Compute sum squared # differences with mean. sqDiff = 0 for i in range(0 ,n): sqDiff += ((a[i] - mean) * (a[i] - mean)) return sqDiff / ndef standardDeviation(arr, n): return math.sqrt(variance(arr, n))# Driver Codearr = [600, 470, 170, 430, 300]n = len(arr)print("Variance: ", int(variance(arr, n)))print("Standard Deviation: ", round(standardDeviation(arr, n), 3))# This code is contributed by Smitha |
C#
// C# program to find variance and// standard deviation of given array.using System;class GFG{ // Function for calculating // variance static float variance(double []a, int n) { // Compute mean (average // of elements) double sum = 0; for (int i = 0; i < n; i++) sum += a[i]; double mean = (double)sum / (double)n; // Compute sum squared // differences with mean. double sqDiff = 0; for (int i = 0; i < n; i++) sqDiff += (a[i] - mean) * (a[i] - mean); return (float)sqDiff / n; } static float standardDeviation(double []arr, int n) { return (float)Math.Sqrt(variance(arr, n)); } // Driver Code public static void Main () { double []arr = {600, 470, 170, 430, 300}; int n = arr.Length; Console.WriteLine( "Variance: " + variance(arr, n)); Console.WriteLine ("Standard Deviation: " + standardDeviation(arr, n)); }}// This code is contributed by vt_m. |
PHP
<?php// PHP program to find variance// and standard deviation of// given array.// Function for calculating.// variancefunction variance( $a, $n){ // Compute mean (average // of elements) $sum = 0; for ( $i = 0; $i < $n; $i++) $sum += $a[$i]; $mean = $sum / $n; // Compute sum squared // differences with mean. $sqDiff = 0; for ( $i = 0; $i < $n; $i++) $sqDiff += ($a[$i] - $mean) * ($a[$i] - $mean); return $sqDiff / $n;}function standardDeviation($arr, $n){ return sqrt(variance($arr, $n));}// Driver Code$arr = array(600, 470, 170, 430, 300);$n = count($arr);echo "Variance: " , variance($arr, $n) , "\n";echo"Standard Deviation: " , standardDeviation($arr, $n) ,"\n";// This code is contributed by anuj_67.?> |
Javascript
<script>// JavaScript program to find variance and// standard deviation of given array. // Function for calculating // variance function variance(a, n) { // Compute mean (average of elements) var sum = 0; for (var i = 0; i < n; i++){ sum += a[i]; } var mean = sum / n; // Compute sum squared // differences with mean. var sqDiff = 0; for (var i = 0; i < n; i++) { sqDiff += (a[i] - mean) * (a[i] - mean); } return sqDiff / n; } function standardDeviation(arr , n) { return Math.sqrt(variance(arr, n)); } // Driver Code var arr = [600, 470, 170, 430, 300] var n = arr.length; document.write( "Variance: " + variance(arr, n) + "<br>"); document.write ("Standard Deviation: " + standardDeviation(arr, n).toFixed(3)); </script> |
Output:
Variance: 21704 Standard Deviation: 147.323
Time complexity of the program is O(n).
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