Question

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

Answer 1

According to the question,
4 =`X/36 and 3 = 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 =`336/100= 3.36.`