# Finding variance without knowing mean?

1. Sep 29, 2008

Hi,

my girlfriend is taking a business statistics class and she had a test today. she got stumped on a question and wrote it down so she could ask me about it when she got back since I'm pretty good at math. I tried solving it but from what i can tell it seems like you would need to know the mean in order to find the variance. the question is below:

Find the Variance:

n = 5
LaTeX Code: \\Sigma x^{2} = 1320
LaTeX Code: \\Sigma x = 80

I expanded out the variance formula. since we run from i=1 to n (where n=5)
I got the formula V = 1320 - 160LaTeX Code: u^{2} + 5LaTeX Code: u^{2} LaTeX Code: /5

where u = the mean.

My girlfriend says that the mean was not specified in the problem. I would have given my answer for the variance as a function of the mean as you can see above, but since this is a business statistics class i have the tendency to believe the teacher is expecting a numerical answer. Does anyone have any insight into how this problem can be solved, or is there not enough information given?

Thank you.

2. Sep 30, 2008

### danago

You can work out the mean. The mean is the just (1/n)Sigma x, the sum of the scores divided by the number of scores.

3. Sep 30, 2008

### HallsofIvy

Staff Emeritus
You need to know the mean but the mean doesn't have to be "given". If $\sum x= 80$ and n= 5, then the mean is $\sum x/n= 80/5= 16$.

4. Sep 30, 2008

### mgb_phys

You can calculate the standard deviation by finding "sum of x" and "sum of x^2" as you go through the data
and calculating (sorry my latex skills are weak today)
sd = 1/n * sqrt ( n*sum_x2 - (sum_x)^2 )

It allows you to only make a single pass through the data - but be careful of rounding errors

Last edited: Sep 30, 2008
5. Sep 30, 2008