数组中给定的数据。找出数据分布的偏斜。 偏斜 是对数据分布不对称性的度量。偏态是统计分布中的一种不对称现象，曲线向左或向右出现扭曲或倾斜。偏度可以量化，以定义分布与正态分布的差异程度。偏度可以计算为
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![图片[1]-统计数据的偏态性-yiteyi-C++库](https://www.yiteyi.com/wp-content/uploads/geeks/geeks_Skewness-1.png)
Where gamma is called skewness sigma is called standard deviation and sigma square can be calculated as
![图片[2]-统计数据的偏态性-yiteyi-C++库](https://media.geeksforgeeks.org/wp-content/uploads/Skewness-1.png)
N is number of population and mu is called mean of data.
例如：
Input : arr[] = {2.5, 3.7, 6.6, 9.1, 9.5, 10.7, 11.9, 21.5, 22.6, 25.2}Output : 0.777001Input : arr[] = {5, 20, 40, 80, 100}Output : 0.0980392
更多关于偏斜的信息 https://en.wikipedia.org/wiki/Skewness https://www.universalclass.com/articles/math/statistics/skewness-in-statistical-terms.htm
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 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; } |
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 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 |
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 call echo 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> |
输出：
0.777001
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