1. Limited time only! Sign up for a free 30min personal 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!

Standard Deviation of test scores

  1. Jul 24, 2010 #1
    1. The problem statement, all variables and given/known data

    The scores of one class on the Unite 2 mathematics test are shown in the table below. Find the population standard deviation of these scores, to the nearest tenth.

    Unit 2 Mathematics Test

    Score - Number of people

    96 - 1
    92 - 2
    84 - 5
    80 - 3
    76 - 6
    72 - 3
    68 - 2

    2. Relevant equations

    standard deviation formula

    3. The attempt at a solution

    I used this website to find the standard deviation for this problem. But my answer is higher than a 100 and i think i made some miscalculations.
  2. jcsd
  3. Jul 24, 2010 #2
    What you are calculating is unbiased standard deviation. I think you have been asked to calculate biased SD for which the formula is

    [tex] \sigma^2 = \overline{(x - \overline{x})^2} [/tex]

    For large data sets, you do not have much issues with the two formulae. This difference in formulae is based on biased/unbiased estimators.
  4. Jul 24, 2010 #3


    User Avatar
    Homework Helper

    You have to find the mean of the scores first. What did you get?

  5. Jul 24, 2010 #4
    The mean is 79.8095.
  6. Jul 24, 2010 #5
    Wouldn't you have to subtract the mean from the test scores?
  7. Jul 24, 2010 #6


    User Avatar
    Homework Helper

    Yes, and take the square and the sum of squares. What did you get?

  8. Jul 30, 2010 #7
    in my understanding (please correct if wrong):

    mean = (96*1+92*2+84*5+80*3+76*6+72*3+68*2)/sum(people) = 79.45

    std deviation = sqrt( sum((score(i)-mean)^2) / (sum(people) - 1)) = 5.57 unbiased
    = sqrt( sum((score(i)-mean)^2) / (sum(people))) = 5.44 biased
  9. Jul 30, 2010 #8


    User Avatar
    Homework Helper

    The mean is correct, but I got 7.54 and 7.36 for the standard deviations.

  10. Jul 31, 2010 #9
    Grateful if you could share the formula please. I am still learning this stuff...
  11. Jul 31, 2010 #10


    User Avatar
    Homework Helper

    Your formula is correct. Are you sure you did not make any mistake in the calculation? Did you multiplied the squares with the number they occur? I guess you did not. You have to sum for all people.

    Last edited: Jul 31, 2010
  12. Jul 31, 2010 #11
    now I see, indeed haven't multiplied differences squared by number of people. It's the same as your result now.

    Thank you!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook