h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Ok i am the most un mathsy person ever, but i have to work out the variance of a data set for psychology.we have been given a formula which is something along the lines of


S^2= sum of X^2 over N, minus Xbar^2


can anyone please help me make sense of this?

mini

I suspect that's a mangled form of the variance, which is simply a way of measuring how widely scattered (or otherwise) your data are. It is the square of what's called the standard deviation.

This looks like a decent explanation: http://davidmlane.com/hyperstat/A16252.html

Mind you, any decent calculator will work it out for you.

Mini,

Let's suppose your data set is this unlikely set of numbers:
1, 2, 3, 4, 5, and 6.

The average or Xbar (or arithmetic mean) is the sum of the data divided by the number of data, so

Xbar = (1+2+3+4+5+6)/6
Xbar = 3.5

Now, as Bagpuss says, we want to see how scattered your data points are from the central measure of 3.5. Maybe 3 and 4 are pretty close, but 1 and 6 are rather far out there. So we want to get the difference in each case.

1 - 3.5 = -2.5
2 - 3.5 = -1.5
3 - 3.5 = -0.5
4 - 3.5 = 0.5
5 - 3.5 = 1.5
6 - 3.5 = 2.5

We are only concerned about how scattered your data points are; we really don't care which direction -positive or negative - they are scattered. It would be great if all the results were positive. We are going to use a sneaky math geek trick to make them all positive - we are going to square all the results.

(-2.5)^2 = 6.25
(-1.5)^2 = 2.25
(-0.5)^2 = 0.25
(0.5)^2 = 0.25
(1.5)^2 = 2.25
(2.5)^2 = 6.25

Now we have a set of numbers which tell us how scattered our original data points are. We'd like to summarize this set of numbers into a single number, in much the same way that a set of numbers can be summarized into an average. So we add them all together, and we probably ought to divide them by something, much like we do when finding an average. First we add:

6.25 + 2.25 + 0.25 + .25 + 2.25 + 6.25 = 17.5

Then, we can divide by the number of data points*.

17.5/6 = 2.91

And that's it. The sample variance is

S^2 = 2.91


Happy Nerd


*We can also divide by one less than the number of data points for some cases, but that's another discussion.

thankyou both for your help.

A maths whizz friend managed to help me through it as explaining maths to me is a little bit like trying to explain quantum physics to a five year old.

mini