Question

In 2016, the mean score on the AP Biology exam was 3.10, with a standard deviation of 1.05. The mean score on the AP US History exam was a 2.74, with a standard deviation of 1.42. What is the combined mean and standard deviation for these exams

Answer 1

the combined mean and standard deviation for these exams are

mean = 5.84

standard deviation = 1.766

Explanation:

Given that;

mean score and standard deviation of AP biology was;

x'1 = 3.10, S1 = 1.05

mean score and standard deviation of AP US History was;

x'2 = 2.74, S1 = 1.42

Now combined mean = x'1 + x'2 = 3.10 + 2.74 = 5.84

standard deviation combined = √( S1² + S2²)

= √( (1.05²) + (1.42)²)

= √( 1.1025 + 2.0164)

= √3.1189

= 1.766

Therefore

the combined mean and standard deviation for these exams are

mean = 5.84

standard deviation = 1.766