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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class Main{
	public static void main(String[] args){
		BufferedReader insBR = new BufferedReader(new InputStreamReader(System.in));

		try{
			List<String> dispList = new ArrayList<String>();
			while(true){

				String strPeople = insBR.readLine();
				if("0".equals(strPeople)){
					break;
				}
				double dbPeople = Double.parseDouble(strPeople);

				//文字列を読み取る。
				String[] strLine = insBR.readLine().split(" ");

				//小数点を鑑みて、double型に変換する。
				List<Double> list = new ArrayList<Double>();
				for(int i = 0; i < strLine.length; i++){
					list.add(Double.parseDouble(strLine[i]));
				}

				//平均値。
				double dbSum = 0.0;
				for(int i = 0; i < list.size(); i++){
					dbSum += list.get(i);
				}
				double dbAverage = dbSum / dbPeople;
				//System.out.println("平均 " + dbAverage);

				//偏差。
				List<Double> devList = new ArrayList<Double>();
				for(int i = 0; i < list.size(); i++){
					double dbAct = list.get(i) - dbAverage;
					devList.add(dbAct);
				}

				//偏差合計。
				dbSum = 0.0;
				for(int i = 0; i < devList.size(); i++){
					double dbAct = devList.get(i);
					dbSum += dbAct * dbAct;
				}
				double dbDisp = dbSum / dbPeople;
				dbDisp = Math.sqrt(dbDisp);
				String strDevation = String.format("%1$.5f", dbDisp);
				dispList.add(strDevation);

			}

			//出力。
			for(int i = 0; i < dispList.size(); i++){
				System.out.println(dispList.get(i));
			}

		}catch(IOException e){
			e.printStackTrace();
		}catch(NumberFormatException e){
			e.printStackTrace();
		}

	}

}