Question

The distributions X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of resulting distribution X + Y?

Answer 1

According to the question,

4 = $\frac{X}{36}$ and 3 = $\frac{Y}{64}$

⇒ X = 4 × 36 and Y = 3 × 64

⇒ X = 144 and Y = 192

Now, X + Y = 144 + 192 = 336

and total number of observations = 36 + 64 = 100

Thus, mean = $\frac{336}{100}=3.36$.