为什么标准差的 MATLAB 计算与手工计算不同？

Question

Matlab:

>> std( [3 2 2 3] )
ans =
    0.5774

外行对标准差的解释Google：

Mean of {3,2,2,3} = 2.5
Deviation from mean for each value = {0.5, 0.5, 0.5, 0.5}
Square of deviation from mean = {0.25, 0.25, 0.25, 0.25}
Mean of the squares = 0.25
Square root of 0.25 = 0.5
Therefore Standard Deviation of {3,2,2,3} = 0.5

我搞砸了什么？我愚蠢地期望这两个数字一致。

Answer 1

Matlab std 计算 corrected standard deviation。来自 help std:

std normalizes Y by (N-1), where N is the sample size. This is the sqrt of an unbiased estimator of the variance of the population from which X is drawn, as long as X consists of independent, identically distributed samples.

所以你有

Square of deviation from mean = {0.25, 0.25, 0.25, 0.25}

那么您不计算偏差的实际均值根，而是 sqrt(sum([0.25 0.25 0.25 0.25])/3)。通常，sum(square of deviation)/(N-1) 表示长度为 N.

的向量

更新： 正如Leonid Beschastny指出的，你可以得到matlab来计算未校正的标准偏差。同样，来自 help std:

Y = std(X,1) normalizes by N and produces the square root of the second moment of the sample about its mean. std(X,0) is the same as std(X).

为什么标准差的 MATLAB 计算与手工计算不同？

Why is MATLAB calculation of standard deviation different than a hand calculation?

matlab

standard-deviation