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
Implementation:
C++
// 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
// 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
# 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 functionarr = [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#
// 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// 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?> |
Javascript
<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
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