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.*;
import java.io.*;

public class Main{
	final static int MOD = 1000000007;
	final static int INF = 1000000000;

	public static void main(String[] args) throws IOException{
		NScanner sc = new NScanner(System.in);
		for(;;){
			int n = sc.nextInt();
			if(n == 0) break;
			int[] a = new int[n];
			double mean = 0.0;
			for(int i = 0; i < n; ++i){
				a[i] = sc.nextInt(); mean += a[i];
			}
			mean /= n;
			double vari = 0.0;
			for(int i = 0; i < n; ++i){
				double dev = a[i] - mean;
				vari += dev*dev/n;
			}
			System.out.printf("%.6f\n", Math.sqrt(vari));
		}
	}

}

class NScanner{

	private BufferedReader br;
	private StringTokenizer tok;

	public NScanner(InputStream is) throws IOException{
		br = new BufferedReader(new InputStreamReader(is));
		getLine();
	}

	private void getLine() throws IOException{
		while(tok == null || !hasNext()){
			tok = new StringTokenizer(br.readLine());
		}
	}

	public boolean hasNext(){
		return tok.hasMoreTokens();
	}

	public String next() throws IOException{
		if(hasNext()){
			return tok.nextToken();
		}else{
			getLine();
			return tok.nextToken();
		}
	}

	public int nextInt() throws IOException{
		if(hasNext()){
			return Integer.parseInt(tok.nextToken());
		}else{
			getLine();
			return Integer.parseInt(tok.nextToken());
		}
	}

	public long nextLong() throws IOException{
		if(hasNext()){
			return Long.parseLong(tok.nextToken());
		}else{
			getLine();
			return Long.parseLong(tok.nextToken());
		}
	}

	public double nextDouble() throws IOException{
		if(hasNext()){
			return Double.parseDouble(tok.nextToken());
		}else{
			getLine();
			return Double.parseDouble(tok.nextToken());
		}
	}
}