# 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
```

## C++

 `// CPP code to find skewness ` `// of statistical data. ` ` `  `#include ` `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

 ` `

Output :

```0.777001
```

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