What does variance measure?

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Answer 1 · 2015-11-10T09:47:47

As the name of the topic indicates variance is a "Measure of Variability"

The variance is a measure of variability. It means that for a set of data you can say: "The higher variance, the more different data".

Examples

$A={1,3,3,3,3,4}$

$bar(x)=(1+3+3+3+3+4)/6=18/6=3$

$sigma^2=1/6*((2-3)^2+4*(3-3)^2+(4-3)^2)$

$sigma^2=1/6*(1+1)$

$sigma^2=1/3$

$B={2,4,2,4,2,4}$

$bar(x)=(2+4+2+4+2+4)/6=18/6=3$

$sigma^2=1/6*(3*(2-3)^2+3*(4-3)^2)$

$sigma^2=1/6*(3*1+3*1)$

$sigma^2=1/6*(6)$

$sigma^2=1$

In set $A$ there are only 2 numbers other then the mean, and the difference is $1$ . The variance is small.

In set $B$ there are no elements equal to mean, and this fact makes the variance bigger.