Seniors at a local high school took both the AP Statistics exam and the AP Literature exam. On the Statistics test, the mean score was 2.4 with a standard deviation of 0.6. On the Literature test, the mean score was 2.65 with a standard deviation of 0.55. If we wanted to look at the combined scores (and assumed the tests were independent), what would their mean and standard deviation be?

5.05, 0.66
5.05, 1.15
5.05, 1.07
5.05, 0.82
5.05, 0.42

Question

Seniors at a local high school took both the AP Statistics exam and the AP Literature exam. On the Statistics test, the mean score was 2.4 with a standard deviation of 0.6. On the Literature test, the mean score was 2.65 with a standard deviation of 0.55. If we wanted to look at the combined scores (and assumed the tests were independent), what would their mean and standard deviation be?

	5.05, 0.66
	5.05, 1.15
	5.05, 1.07
	5.05, 0.82
	5.05, 0.42

anonymous · Answer

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anonymous · Answer

so is that the answer to the question? @burgandy

anonymous · Answer

Yes. Now give me BA

kirbykirby · Answer

You can add the 2 means together to get $${2.4+2.65}=5.05$$For the standard deviation though, we can't add them together, we can only add the squares of the standard deviations together (i.e the variances). Then you can square root that result. 
$$0.6^2+0.55^2$$
So, the standard deviation is now:
$\sqrt{0.6^2+0.55^2}$

If you know about random variables, this is because for independent random variables X and Y:
$Var(X+Y)=Var(X)+Var(Y)$ but
$\sqrt{Var(X+Y)}\ne\sqrt{Var(X)}+\sqrt{Var(Y)}$