方差的計算，如果不太計較精度的話，可以使用 Apache 的 commons-math3（http://commons.apache.org/proper/commons-math/）提供的 Variance 類。不過畢竟 Variance 是使用 double 進行計算，會有精度損失，所以自己寫了個計算方差的工具類，採用 BigDecimal 進行計算，並且可以自己指定精度值，程式碼如下：

package com.frank.test.variance;

import java.math.BigDecimal;

import com.google.common.base.Preconditions;

/**
 * 方差計算工具類。
 * 
 * @author frank
 */
public final class VarianceUtils {
	/**
	 * 預設精度
	 */
	private static final int DEFAULT_SCALE = 64;
	private VarianceUtils() {}
	
	public static BigDecimal variance(byte[] arr) {
		Preconditions.checkNotNull(arr);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr);
	}
	
	public static BigDecimal variance(byte[] arr, int scale) {
		Preconditions.checkNotNull(arr);
		Preconditions.checkArgument(scale > 0, "scale must be positive: " + scale);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr, scale);
	}
	
	public static BigDecimal variance(char[] arr) {
		Preconditions.checkNotNull(arr);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr);
	}
	
	public static BigDecimal variance(char[] arr, int scale) {
		Preconditions.checkNotNull(arr);
		Preconditions.checkArgument(scale > 0, "scale must be positive: " + scale);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr, scale);
	}
	
	public static BigDecimal variance(int[] arr) {
		Preconditions.checkNotNull(arr);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr);
	}
	
	public static BigDecimal variance(int[] arr, int scale) {
		Preconditions.checkNotNull(arr);
		Preconditions.checkArgument(scale > 0, "scale must be positive: " + scale);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr, scale);
	}
	
	public static BigDecimal variance(long[] arr) {
		Preconditions.checkNotNull(arr);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr);
	}
	
	public static BigDecimal variance(long[] arr, int scale) {
		Preconditions.checkNotNull(arr);
		Preconditions.checkArgument(scale > 0, "scale must be positive: " + scale);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr, scale);
	}
	
	public static BigDecimal variance(float[] arr) {
		Preconditions.checkNotNull(arr);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr);
	}
	
	public static BigDecimal variance(float[] arr, int scale) {
		Preconditions.checkNotNull(arr);
		Preconditions.checkArgument(scale > 0, "scale must be positive: " + scale);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr, scale);
	}
	
	public static BigDecimal variance(double[] arr) {
		Preconditions.checkNotNull(arr);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr);
	}
	
	public static BigDecimal variance(double[] arr, int scale) {
		Preconditions.checkNotNull(arr);
		Preconditions.checkArgument(scale > 0, "scale must be positive: " + scale);
		
		String[] strArr = new String[arr.length];
		for (int i = 0; i < arr.length; i++) {
			strArr[i] = String.valueOf(arr[i]);
		}
		return variance(strArr, scale);
	}
	
	private static BigDecimal variance(String[] arr) {
		return variance(arr, DEFAULT_SCALE);
	}
	
	private static BigDecimal variance(String[] arr, int scale) {
		BigDecimal sum = BigDecimal.ZERO;
        for (int i = 0; i < arr.length; i++) {
            sum = sum.add(new BigDecimal(arr[i]));
        }
        BigDecimal meanNum = sum.divide(new BigDecimal(arr.length), scale, BigDecimal.ROUND_HALF_DOWN);
        
        BigDecimal tmp = null;
        BigDecimal tmpSum = BigDecimal.ZERO;
        for (int i = 0; i < arr.length; i++) {
            tmp = meanNum.subtract(new BigDecimal(arr[i]));
            tmpSum = tmpSum.add(tmp.multiply(tmp));
        }
        BigDecimal vari = tmpSum.divide(new BigDecimal(arr.length - 1), scale, BigDecimal.ROUND_HALF_DOWN);
        return new BigDecimal(trimZero(vari.toString()));
	}
	
	/**
	 * 去除小數中後面多餘的0
	 * 
	 * @param str
	 * @return
	 */
	private static String trimZero(String str) {
		if (!str.contains(".")) {
			return str;
		}
		
		StringBuilder ret = new StringBuilder();
		char[] chars = str.toCharArray();
		for (int i = chars.length - 1; i >= 0; i--) {
			char ch = chars[i];
			if (ch != '0') {
				ret.append(ch);
			}
		}
		return ret.reverse().toString();
	}
}
 

該工具類是使用最基本的方差計算公式進行計算的，如果要使用流式方式計算方差，可以參考以下文章：