Question

The mean of two samples of the sizes 250 and 320 were found to be 20,12 respectively. Their standard deviations were 2 & 5, respectively. Find the variance of combined sample of size 650.

(a) 10.23

(b) 32.5

(c) 65

(d) 26.17

I got this question in an internship interview.

This interesting question is from Statistics topic in portion Statistics of Mathematics – Class 11

Answer 1

The correct answer is (d) 26.17

Explanation: Combined Mean = X = (n1x1 + n2x2)/(n1 + n2) = (250 × 20 + 320 × 12)/650 = 13.6

Let d1 = x1 – X = 20-13.6 = 6.4, d2 = x2 – X = 12-13.6 = -1.6

Variance = [250(6.4 + 40.96) + 320(13.6 + 2.56)]/650 = 26.17.