How to calculate sample and population variances in Matlab?

Question

I have a vector a

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

And I want to calculate the std and mean by

Answer 1

Try this:

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


var =

  335.2111

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

For a complete explanation you can read here.

From the matlab documentation,

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.

but

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).

so that

>> var(a,1)

ans =

  301.6900

Answer 2

An unbiased sample variance is given by:

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

ans =

  335.2111