Skewness of statistical data

Given data in array. Find skewness of the data distribution.

Skewness is a measure of the asymmetry of a data distribution. Skewness is 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++

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// 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 function
int 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;
}

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Java

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// 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

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Python3

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# 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 call
print('%.6f'%skewness(arr, n))
  
# This code is contributed by shubhamsingh10

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C#

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// 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

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PHP

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<?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 call
echo skewness($arr, $n);
  
  
// This code is contributed by vt_m
?>

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Output :

0.777001

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Improved By : vt_m, SHUBHAMSINGH10

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