如何在Matlab中计算样本和总体方差? [英] How to calculate sample and population variances in Matlab?

问题描述

我有一个向量a

a = [86 100 41 93 75 61 76 92 88 97]

我想通过以下方式计算std和mean 我自己:

And I want to calculate the std and mean by myself:

>> mean(a)

ans =

   80.9000

>> std(a)^2

ans =

  335.2111

但是当我这样做时，我得到了错误的方差:

But when I do it like that I get wrong variance:

>> avg = mean(a)

avg =

   80.9000

>> var = sum(a.^2)/length(a) - avg^2

var =

  301.6900

我在这里想念什么?

为什么sum(a.^2)/length(a) - avg^2 != std(a)^2吗?

推荐答案

尝试一下:

var = sum(a.^2)/(length(a)-1) - (length(a))*mean(a)^2/(length(a)-1)


var =

  335.2111

var计算为(无偏)样本，而不是总体方差.

var is computed as (unbiased) sample, not population variance.

有关完整的解释，您可以在此处阅读.

For a complete explanation you can read here.

从matlab文档中，

From the matlab documentation,

VAR通过N-1归一化Y，其中N是样本大小.这是一 X是的总体的方差的无偏估计量 绘制，只要X由独立且分布均匀的 样本.

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

但是

Y = VAR(X，1)通过N归一化并产生第二个矩 关于其均值的样本. VAR(X，0)与VAR(X)相同.

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

这样

>> var(a,1)

ans =

  301.6900

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