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

Answer 1

The answer is 5.05 and 0.82

As standard deviation is the square root of variance, so we take the square root of variance to get the new standard deviation.

Sum of means = 2.45+2.65 = 5.05
Combined mean = 5.05/2 = 2.525
variance = 0.36+0.3025 = 0.6625

combined standard deviation = square root (0.6625) = 0.814 ~ .82