Problem:
Standard Deviation

You have final scores of an examination for n students. Calculate standard deviation of the scores s1, s2 ... sn.

The variance α2 is defined by

α2 = (∑ni=1(si - m)2)/n

where m is an average of si.

The standard deviation of the scores is the square root of their variance.

Input

The input consists of multiple datasets. Each dataset is given in the following format:

n
s1 s2 ... sn

The input ends with single zero for n.

Output

For each dataset, print the standard deviation in a line. The output should not contain an absolute error greater than 10-4.

Constraints

n ≤ 1000

0 ≤ si ≤ 100

Sample Input

5
70 80 100 90 20
3
80 80 80
0

Sample Output

27.85677655
0.00000000

Solution in JAVA (judge verdict: Accepted)



import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		while (true) {
			int n = sc.nextInt();
			int[] s = new int[n];
			int sum = 0;

			if (n == 0) {
				break;
			}

			for (int i = 0; i < n; i++) {
				s[i] = sc.nextInt();
//点数を合計する
				sum += s[i];
			}
//平均を出す
			double ave = sum / (double) n;
			double a = 0;
			for (int i = 0; i < n; i++) {
//偏差求める
				a += (s[i] - ave) * (s[i] - ave);
			}
//分散を求める
			a = a / (double) n;
//分散の正の平方根を計算
			System.out.println(Math.sqrt(a));
		}

	}
}