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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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. 
?> 

Output :

Variance: 21704
Standard Deviation: 147.323

Time complexity of the program is O(n).

This article is contributed by Himanshu Ranjan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python 3

C#

PHP

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