# Finding variance without knowing mean?

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.

danago
Gold Member
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.

HallsofIvy
Homework Helper
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 $\sum x/n= 80/5= 16$.

mgb_phys
Homework Helper
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:
wow thanks everyone. That was really dumb of me to not realize that the mean was right before my eyes.