The **standard deviation **is the measure of how spread out numbers are. Its symbol is sigma**(** **σ ). **It is the square root of variance. The task is to calculate the standard deviation of some numbers.

Consider an example that consists of 6 numbers and then to calculate the standard deviation, first we need to calculate the sum of 6 numbers, and then the mean will be calculated. Then the standard deviation will be calculated using the standard deviation formula.

Standard deviation = square root of ∑(Xwhere, X_{i}- ų)^{2}/ N_{i }= each element of the array ų = mean of the elements of the array N = Number of elements ∑ = Sum of the each element

Input :[12, 32, 11, 55, 10, 23, 14, 30]Output :14.438988Input :[10, 12, 22, 34, 21]Output :8.541663

**Approach: Using Mathematical Formula**

- First, create a class called
**calculateSD2** - Then create the main method and then in the main method create an object of the above class and call it using the object.
- Then declare an array in this class with the values given in the above example.
- Now, in order to iterate through the array, we need to find the size of the array.
- Now, use the for-loop and iterate through this array and increment it by 1 as we need to print all the elements of the array.
- Then, again use the for-loop and iterate through the array in order to calculate the sum of the elements of the array.
- After that, the mean will be calculated by mean = sum / n, where n is the number of elements in the array.
- Now, the standard deviation will be calculated with the help of mean, which is done by iterating through for-loop again and with the help of Mathematical predefined methods like Math.pow and Math.sqrt.
- After that, the value will be returned by that class and then print.

## Java

`// Java program to calculate the standard deviation` ` ` `class` `calculateSD2 {` ` ` `double` `sum = ` `0.0` `;` ` ` `double` `standardDeviation = ` `0.0` `;` ` ` `double` `mean = ` `0.0` `;` ` ` `double` `res = ` `0.0` `;` ` ` `double` `sq = ` `0.0` `;` ` ` ` ` `double` `SD()` ` ` `{` ` ` `int` `[] arr = { ` `12` `, ` `32` `, ` `11` `, ` `55` `, ` `10` `, ` `23` `, ` `14` `, ` `30` `};` ` ` `int` `n = arr.length;` ` ` ` ` `System.out.println(` `"Elements are:"` `);` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) {` ` ` `System.out.println(arr[i]);` ` ` `}` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) {` ` ` `sum = sum + arr[i];` ` ` `}` ` ` ` ` `mean = sum / (n);` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) {` ` ` ` ` `standardDeviation` ` ` `= standardDeviation + Math.pow((arr[i] - mean), ` `2` `);` ` ` ` ` `}` ` ` ` ` `sq = standardDeviation / n;` ` ` `res = Math.sqrt(sq);` ` ` `return` `res;` ` ` `}` `}` ` ` `public` `class` `Standard {` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` ` ` `calculateSD2 calsd = ` `new` `calculateSD2();` ` ` `double` `res = calsd.SD();` ` ` ` ` `System.out.format(` `"Standard Deviation = %.6f"` `, res);` ` ` `}` `}` |

**Output**

Elements are: 12 32 11 55 10 23 14 30 Standard Deviation = 14.438988

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