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: O(n)

Auxiliary Space: O(1)

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

Approach#2: Using sum()

This approach calculates the mean, variance, and standard deviation of the input array without using any external library. It first calculates the mean of the array by dividing the sum of the elements by the number of elements in the array. Then, it calculates the variance by iterating over each element of the array, subtracting the mean from it, squaring the result, and summing up all the squares. Finally, it calculates the standard deviation by taking the square root of the variance.

Algorithm

1. Calculate the mean of the array by dividing the sum of the elements by the number of elements in the array.
2. Calculate the variance by iterating over each element of the array:
a. Subtract the mean from the element.
b. Square the result of step (2a).
c. Sum up all the squares obtained in step (2b).
d. Divide the sum obtained in step (2c) by the number of elements in the array.
3. Calculate the standard deviation by taking the square root of the variance.
4. Print the variance and standard deviation.

Python3

# Input array
arr = [7, 7, 8, 8, 3]

# Calculate the mean of the array
mean = sum(arr) / len(arr)

# Calculate the variance and standard deviation
variance = sum((i - mean) ** 2 for i in arr) / len(arr)
std_deviation = variance ** 0.5

# Print the results
print("Variance =", int(variance))
print("Standard Deviation =", int(std_deviation))

Output

Variance = 3
Standard Deviation = 1

Time complexity: O(n), where n is the number of elements in the input array. The code iterates over each element of the input array once to calculate the mean and again to calculate the variance.

Auxiliary Space:  O(1), as it does not use any additional data structure to store the intermediate results.