# Math Help - Help with variance

1. ## Help with variance

Looking to find a simple way to find the variance of a sample data set.

Is the only way to square the numbers,add them up and use the formula or is there a way on my calculator?

Also I see a easy formula shown in the pic below but, Where does the x value come from I have the arrow pointing to?

2. ## Re: Help with variance

Hi Asylum1!

The "x" in your formula for variance represents each value of your data set, that you are supposed to fill in one by one.

There is probably a way on your calculator.
Most calculators have a function to show the statistical descriptives of a sample set.
Variance is just one of them.

3. ## Re: Help with variance

So your saying the only way to do this is like this?

4. ## Re: Help with variance

There are a couple of ways of doing it.

Suppose you have the the sample 3, 4, 5.
Its average is $\bar x = 4$.

You can calculate its sample variance by the first formula you gave:

$s^2 = {(3-4)^2 + (4-4)^2 + (5-4)^2 \over 3 - 1}$

Or by the formula you gave just now (actually, I'm computing $s^2$ instead of $\sigma^2$):

$s^2 = {(3^2 + 4^2 + 5^2) - (3 + 4 + 5)^2 / 3\over 3 - 1}$

Or by a slight modification of it:

$s^2 = {(3^2 + 4^2 + 5^2) - 3 \cdot 4^2\over 3 - 1}$

5. ## Re: Help with variance

Found a real simple way to find the variance on my calculator.

All you have to do is square the standard deviation.

6. ## Re: Help with variance

Yep. That will do the trick.

Cheers!