Question

What does variance measure?

Answer 1

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

Explanation:

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 set of data with small differences.

`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`

• A set of data with bigger differences.

`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.