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Homework Help: 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


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    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


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    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


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    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


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    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!
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