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 variance int 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 Code int 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 variance def 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 / n def standardDeviation(arr, n): return math.sqrt(variance(arr, n)) # Driver Code arr = [ 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. // variance function 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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