1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding variance without knowing mean?

  1. Sep 29, 2008 #1

    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. jcsd
  3. Sep 30, 2008 #2


    User Avatar
    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.
  4. Sep 30, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    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].
  5. Sep 30, 2008 #4


    User Avatar
    Science Advisor
    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: Sep 30, 2008
  6. Sep 30, 2008 #5
    wow thanks everyone. That was really dumb of me to not realize that the mean was right before my eyes.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Finding variance without knowing mean?
  1. Find the Variance (Replies: 9)