Question

a teacher teaches two sections (A and B) of a class. Both sections have a mean score of 75. Section A only has 5 students and they all received a score of 75, while section B has 15 students with a mean score of 75 with a variance of 12. What is the standard deviation of the combined class (N=20, treat as the population).
a)9 b)6 c)4 d)3 e)2

So as a result section A has zero for the variance. I am having trouble figuring out the correct equation to solve this problem.

Answer 1

Variance = Σx^2/N, where x = X-μ. Since Σx^2 = 0 for the first group, it will contribute nothing to the Σx^2, so that term will remain the same for the combined class, but the N will increase from 15 to 20.

For the second group, since Variance = Σx^2/N,

Σx^2 = Variance * N = 12 * 15 = 180

Thus for the second group, variance = 180/20 = 9

However, the standard deviation is the square root of the variance. You should be able to calculate that.

I hope this helps. Thanks for asking.