Skewness of statistical data - GeeksforGeeks

25 May, 2021
Given data in an array. Find skewness of the data distribution.Skewness is a measure of the asymmetry of data distribution. Skewness is an asymmetry in a statistical distribution, in which the curve appears distorted or skewed either to the left or to the right. Skewness can be quantified to define the extent to which a distribution differs from a normal distribution. Skewness can be calculated as  
 
Where gamma is called skewness
      sigma is called standard deviation and sigma square can be calculated as
      
      N is number of population and
      mu is called mean of data.  
Examples :  
Input : arr[] = {2.5, 3.7, 6.6, 9.1, 9.5, 10.7, 11.9, 21.5, 22.6, 25.2}
Output : 0.777001

Input : arr[] = {5, 20, 40, 80, 100}
Output : 0.0980392
For more about skewness https://en.wikipedia.org/wiki/Skewness https://www.universalclass.com/articles/math/statistics/skewness-in-statistical-terms.htm 
 
C++
Java
Python3
C#
PHP
Javascript
// CPP code to find skewness// of statistical data. #include<bits/stdc++.h>using namespace std; // Function to calculate// mean of data.float mean(float arr[], int n){    float sum = 0;    for (int i = 0; i < n; i++)        sum = sum + arr[i];           return sum / n;} // Function to calculate standard// deviation of data.float standardDeviation(float arr[],                        int n){    float sum = 0;         // find standard deviation    // deviation of data.    for (int i = 0; i < n; i++)        sum = (arr[i] - mean(arr, n)) *              (arr[i] - mean(arr, n));                   return sqrt(sum / n);} // Function to calculate skewness.float skewness(float arr[], int n){      // Find skewness using above formula    float sum = 0;    for (int i = 0; i < n; i++)        sum = (arr[i] - mean(arr, n)) *              (arr[i] - mean(arr, n)) *              (arr[i] - mean(arr, n));                 return sum / (n * standardDeviation(arr, n) *                 standardDeviation(arr, n) *                 standardDeviation(arr, n) *                 standardDeviation(arr, n));} // Driver functionint main(){    float arr[] = {2.5, 3.7, 6.6, 9.1,                   9.5, 10.7, 11.9, 21.5,                   22.6, 25.2};                        // calculate size of array.    int n = sizeof(arr)/sizeof(arr[0]);         // skewness Function call    cout << skewness(arr, n);         return 0;}
// java code to find skewness// of statistical data.import java.io.*; class GFG {         // Function to calculate    // mean of data.    static double mean(double arr[], int n)    {        double sum = 0;                 for (int i = 0; i < n; i++)            sum = sum + arr[i];                 return sum / n;    }         // Function to calculate standard    // deviation of data.    static double standardDeviation(double arr[],                                            int n)    {                 double sum = 0 ;                 // find standard deviation        // deviation of data.        for (int i = 0; i < n; i++)            sum = (arr[i] - mean(arr, n)) *                        (arr[i] - mean(arr, n));                         return Math.sqrt(sum / n);    }         // Function to calculate skewness.    static double skewness(double arr[], int n)    {        // Find skewness using        // above formula        double sum = 0;                 for (int i = 0; i < n; i++)            sum = (arr[i] - mean(arr, n)) *                    (arr[i] - mean(arr, n)) *                        (arr[i] - mean(arr, n));                             return sum / (n * standardDeviation(arr, n) *                          standardDeviation(arr, n) *                          standardDeviation(arr, n) *                          standardDeviation(arr, n));    }         // Driver function    public static void main (String[] args)    {        double arr[] = { 2.5, 3.7, 6.6, 9.1,                        9.5, 10.7, 11.9, 21.5,                                   22.6, 25.2 };                                 // calculate size of array.        int n = arr.length;                 // skewness Function call        System.out.println(skewness(arr, n));    }} //This code is contributed by vt_m
# Python3 code to find skewness# of statistical data.from math import sqrt # Function to calculate# mean of data.def mean(arr, n):         summ = 0    for i in range(n):        summ = summ + arr[i]        return summ / n # Function to calculate standard# deviation of data.def standardDeviation(arr,n):         summ = 0         # find standard deviation    # deviation of data.    for i in range(n):        summ = (arr[i] - mean(arr, n)) *(arr[i] - mean(arr, n))         return sqrt(summ / n) # Function to calculate skewness.def skewness(arr, n):         # Find skewness using above formula    summ = 0    for i in range(n):        summ = (arr[i] - mean(arr, n))*(arr[i] - mean(arr, n))*(arr[i] - mean(arr, n))    return summ / (n * standardDeviation(arr, n) *standardDeviation(arr, n) *standardDeviation(arr, n) * standardDeviation(arr, n)) # Driver function arr = [2.5, 3.7, 6.6, 9.1,9.5, 10.7, 11.9, 21.5,22.6, 25.2]                 # calculate size of array.n = len(arr) # skewness Function callprint('%.6f'%skewness(arr, n)) # This code is contributed by shubhamsingh10
// C# code to find skewness// of statistical data.using System; class GFG {         // Function to calculate    // mean of data.    static float mean(double []arr, int n)    {        double sum = 0;                 for (int i = 0; i < n; i++)            sum = sum + arr[i];                 return (float)sum / n;    }         // Function to calculate standard    // deviation of data.    static float standardDeviation(double []arr,                                            int n)    {                 double sum = 0 ;                 // find standard deviation        // deviation of data.        for (int i = 0; i < n; i++)            sum = (arr[i] - mean(arr, n)) *                  (arr[i] - mean(arr, n));                         return (float)Math.Sqrt(sum / n);    }         // Function to calculate skewness.    static float skewness(double []arr, int n)    {        // Find skewness using        // above formula        double sum = 0;                 for (int i = 0; i < n; i++)            sum = (arr[i] - mean(arr, n)) *                  (arr[i] - mean(arr, n)) *                  (arr[i] - mean(arr, n));                             return (float)sum / (n * standardDeviation(arr, n) *                        standardDeviation(arr, n) *                        standardDeviation(arr, n) *                        standardDeviation(arr, n));    }         // Driver function    public static void Main ()    {        double []arr = { 2.5, 3.7, 6.6, 9.1,                        9.5, 10.7, 11.9, 21.5,                                22.6, 25.2 };                                 // calculate size of array.        int n = arr.Length;                 // skewness Function call        Console.WriteLine(skewness(arr, n));    }} // This code is contributed by vt_m
<?php// PHP code to find skewness// of statistical data. // Function to calculate// mean of data.function mean( $arr, $n){    $sum = 0;    for ($i = 0; $i < $n; $i++)        $sum = $sum + $arr[$i];    return $sum / $n;} // Function to calculate standard// deviation of data.function standardDeviation($arr, $n){    $sum = 0;         // find standard deviation    // deviation of data.    for ($i = 0; $i < $n; $i++)        $sum = ($arr[$i] - mean($arr, $n)) *               ($arr[$i] - mean($arr, $n));                 return sqrt($sum / $n);} // Function to calculate skewness.function skewness($arr, $n){    // Find skewness using above formula    $sum = 0;    for ($i = 0; $i < $n; $i++)        $sum = ($arr[$i] - mean($arr, $n)) *               ($arr[$i] - mean($arr, $n)) *               ($arr[$i] - mean($arr, $n));                return $sum / ($n * standardDeviation($arr, $n) *                        standardDeviation($arr, $n) *                        standardDeviation($arr, $n) *                        standardDeviation($arr, $n));} // Driver Code$arr = array(2.5, 3.7, 6.6, 9.1, 9.5,             10.7, 11.9, 21.5, 22.6, 25.2);                 // calculate size of array.$n = count($arr); // skewness Function callecho skewness($arr, $n);  // This code is contributed by vt_m?>
<script>     // JavaScript code to find skewness    // of statistical data.         // Function to calculate    // mean of data.    function mean(arr, n)    {        let sum = 0;                   for (let i = 0; i < n; i++)            sum = sum + arr[i];                   return sum / n;    }           // Function to calculate standard    // deviation of data.    function standardDeviation(arr, n)    {                   let sum = 0 ;                   // find standard deviation        // deviation of data.        for (let i = 0; i < n; i++)            sum = (arr[i] - mean(arr, n)) *                  (arr[i] - mean(arr, n));                           return Math.sqrt(sum / n);    }           // Function to calculate skewness.    function skewness(arr, n)    {        // Find skewness using        // above formula        let sum = 0;                   for (let i = 0; i < n; i++)            sum = (arr[i] - mean(arr, n)) *                  (arr[i] - mean(arr, n)) *                  (arr[i] - mean(arr, n));                               return sum / (n * standardDeviation(arr, n) *                        standardDeviation(arr, n) *                        standardDeviation(arr, n) *                        standardDeviation(arr, n));    }         let arr =    [ 2.5, 3.7, 6.6, 9.1, 9.5, 10.7, 11.9, 21.5, 22.6, 25.2 ];                               // calculate size of array.    let n = arr.length;     // skewness Function call    document.write(skewness(arr, n).toFixed(6));     </script>
Output:  
0.777001
 
vt_m
SHUBHAMSINGH10
mukesh07
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