Standard Deviation of test scores

[priscilla98]

Homework Statement

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

Homework Equations

standard deviation formula

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.
http://www.gcseguide.co.uk/standard_deviation.htm

 

[praharmitra]

What you are calculating is unbiased standard deviation. I think you have been asked to calculate biased SD for which the formula is

$$\sigma^2 = \overline{(x - \overline{x})^2}$$

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

 

[ehild]

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

ehild

 

[priscilla98]

The mean is 79.8095.

 

[priscilla98]

Wouldn't you have to subtract the mean from the test scores?

 

[ehild]

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

ehild

 

[kastelian]

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

 

[ehild]

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

ehild

 

[kastelian]

ehild:
Grateful if you could share the formula please. I am still learning this stuff...

 

[ehild]

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.

ehild

 

[kastelian]

now I see, indeed haven't multiplied differences squared by number of people. It's the same as your result now.

Thank you!