# variance value

• May 26th 2013, 04:58 AM
anthonye
variance value
Hi;

I know the formula for variance and that a low value means the data is more compact
and a larger value means spread out more.

But what does the value actually relate to?
• May 26th 2013, 07:08 AM
HallsofIvy
Re: variance value
Pretty much just what you said: how much the data "varies" or is spread out. Essentially, it tells us how "random" the data is.
• May 26th 2013, 11:07 AM
MINOANMAN
Re: variance value
It is a measure of spread
for more details look here..:
Variance - Wikipedia, the free encyclopedia
• May 27th 2013, 11:20 AM
anthonye
Re: variance value
Variance,average distance to the mean squared so lets say I have a data set of

3,4,6,7 Therfore mean=5

variance=2.5. I get average distance as 2+1+1+2=6/4 1.5squared equals 2.25.

Why is this?
• May 27th 2013, 12:11 PM
Shakarri
Re: variance value
The average of several numbers which have been squared is not equal to the average of the numbers then squared.

Suppose you have 2 numbers a and b
The average of their squares is $\frac{a^2+b^2}{2}$

The square of their average is $(\frac{a+b}{2})^2=\frac{a^2+2ab+b^2}{4}$

You can see that they are different values.