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.ArrayList;
import java.util.Scanner;

public class Main {

	static final int END_SIGN = 0;

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

		// 標準偏差値のリスト
		ArrayList<Double> standardDeviationList = new ArrayList<Double>();

		int inputCount;
		// 得点の件数を入力、0で終了
		while (EndDecision(inputCount = sc.nextInt())) {
			// 得点リスト
			ArrayList<Double> scoreList = new ArrayList<Double>();
			for (int i = 0; i < inputCount; i++) {
				scoreList.add(sc.nextDouble());
			}
			// 標準偏差値を計算し、標準偏差値リストに追加
			standardDeviationList.add(StandardDeviationCalculation(scoreList));
		}

		// 出力
		for (double value : standardDeviationList) {
			System.out.println(value);
		}

	}

	// リストから標準偏差値を返す
	private static double StandardDeviationCalculation(ArrayList<Double> List) {
		double standardDeviation = 0;
		ArrayList<Double> differenceFromAverageList = new ArrayList<Double>();
		for (double i : List)
			differenceFromAverageList.add(Math.pow((Average(List)) - i, 2));
		// 平均との差の２乗の合計から平均を平方根計算し標準偏差値を求める
		standardDeviation = Math.sqrt(Average(differenceFromAverageList));

		return standardDeviation;
	}

	// リストから平均を返す
	private static double Average(ArrayList<Double> List) {
		double sum = 0;
		for (double d : List) {
			sum += d;
		}
		return sum / List.size();
	}

	// 終了判定
	private static boolean EndDecision(int i) {
		if (i == END_SIGN) {
			return false;
		} else {
			return true;
		}
	}

}