StdDev | Topcoder Archive

Problem Statement

The standard deviation of a group of numbers is a very useful statistic in many settings. It measures how spread out a group of numbers is and shows up in all sorts of statistical analyses.

To find the standard deviation of a group of numbers, you must use the following formula:

StdDev = sqrt( sum over all elements[ (nums_i - mean)^2 ]/N )

Here, nums_i represents the i^th element of the input int[], nums. mean represents the average of all the elements in nums. N represents the number of elements in nums. The character '^' denotes exponentiation. Your method should compute this standard deviation, and return the result as a double.

Definition

Class:: StdDev
Method:: stdDev
Parameters:: int[]
Returns:: double
Method signature:: double stdDev(int[] nums)
(be sure your method is public)

Notes

You do not need to worry about small rounding errors. As long as your result is within (10^-9*the exact result) of the exact result your solution will be evaluated as correct. In other words, as long as the first 9 digits are correct, your result will be considered correct. Floating point arithmetic is plenty accurate to solve this problem without worrying about rounding.

Constraints

nums will contain between 1 and 50 elements, inclusive.
Each element of nums will be between -1,000,000,000 and 1,000,000,000, inclusive.

Examples

```
{0,2,3,4,6}
```
```
Returns: 2.0
```
The mean is 3, so sum over all elements[ (numsi - mean)^2 ] = 9 + 1 + 0 + 1 + 9 = 20 So, the standard deviation is sqrt(20/5) = 2.
```
{1,2,3,4}
```
```
Returns: 1.118033988749895
```

{15672,-458661,4567231,-48981111,4567231,-1000000000}

Returns: 3.7015176854905784E8

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