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: Runtime Error)

import java.math.BigDecimal;
import java.math.MathContext;
import java.util.Scanner;

public class Main {

    public BigDecimal pow(BigDecimal value) {
        return value.multiply(value);
    }

    public static BigDecimal sqrt(BigDecimal a, int scale){
        BigDecimal x = new BigDecimal(
                Math.sqrt(a.doubleValue()), MathContext.DECIMAL64);
        if(scale < 17) return x;

        BigDecimal b2 = new BigDecimal(2);
        for(int tempScale = 16; tempScale < scale; tempScale *= 2){
            x = x.subtract(
                    x.multiply(x).subtract(a).divide(
                    x.multiply(b2), scale, BigDecimal.ROUND_HALF_EVEN));
        }
        return x;
    }

    public BigDecimal average(int[] values) {
        int sum = 0;
        for (int i=0; i<values.length; i++) {
            sum += values[i];
        }
        return new BigDecimal(sum).divide(new BigDecimal(values.length));
    }

    public BigDecimal var(int[] values) {
        BigDecimal sum = BigDecimal.ZERO;
        for (int i=0; i<values.length; i++) {
            sum = sum.add(pow(new BigDecimal(values[i]).subtract(average(values))));
        }

        return sum.divide(new BigDecimal(values.length), 2, BigDecimal.ROUND_HALF_UP);
    }

    public BigDecimal std(int values[]) {
        return sqrt(var(values), 3);
    }

    public static void main(String[] args) {

    	Scanner sc = new Scanner(System.in);

        int count = 0;
        int size = 0;
        int[] values = new int[count];

        Main m = new Main();
        while(true) {
        	count = sc.nextInt();
        	if(count == 0) break;
            size = count;
            values = new int[size];
        	for(int i=0; i<count; i++) {
        		values[i] = sc.nextInt();
        	}
        	System.out.println(m.std(values));
        }

        sc.close();
    }
}