Finding variance without knowing mean?

  • #1
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.
 

Answers and Replies

  • #2
danago
Gold Member
1,122
4
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
HallsofIvy
Science Advisor
Homework Helper
41,847
964
You need to know the mean but the mean doesn't have to be "given". If [itex]\sum x= 80[/itex] and n= 5, then the mean is [itex]\sum x/n= 80/5= 16[/itex].
 
  • #4
mgb_phys
Science Advisor
Homework Helper
7,819
13
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:
  • #5
wow thanks everyone. That was really dumb of me to not realize that the mean was right before my eyes.
 

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