SOLUTION: A class has an equal number of boys and girls. The boys all got 85% on a test and the girls all got 91%. What are the mean and standard deviation of the test scores for the entire

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Question 1022940: A class has an equal number of boys and girls. The boys all got 85% on a test and the girls all got 91%. What are the mean and standard deviation of the test scores for the entire class?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
We treat the entire class as a population.
Let n = number of boys = number of girls ==> total number of students is 2n.
==> The mean of the test scores would be mu+=+%280.85n%2B0.91n%29%2F%282n%29+=+%281.76n%29%2F%282n%29+=+0.88, or highlight%2888%29%.
To find the standard deviation, use the formula sigma%5E2+=+%281%2F%282n%29%29sum%28x%5Bi%5D%5E2%2C+1%2C+2n+%29+-+mu%5E2 for the population variance.
==> sigma%5E2+=+%281%2F%282n%29%29%28n%280.85%5E2%29%2Bn%280.91%5E2%29%29+-+0.88%5E2
==> sigma%5E2+=+%280.85%5E2%2B0.91%5E2%29%2F2+-+0.88%5E2+=+0.0009
==> sigma+=+0.03, to three decimal places.
The standard deviation is highlight%280.03%29.
(Note that both averages of 85% and 91% are exactly one standard deviation from the mean!)