NDA 2020 Maths · Mathematics · Statistics · hard

Two groups each have 10 observations. The first has mean 4 and variance 2, the second has mean 6 and variance 2. The variance of the combined 20…

Single correct option

Two groups each have

10

observations. The first has mean

4

and variance

2

, the second has mean

6

and variance

2

. The variance of the combined

20

observations is

Show answer and solution

Answer: (A) $3$

The combined mean is

5

. The combined variance is the average within-group variance plus the variance between the group means:

\dfrac{10(2+1^2)+10(2+1^2)}{20}=3

, since each group mean differs from

5

1

. The value

2

ignores the spread between the groups, while

1

counts only that spread. Pooling variances without the mean-shift term is the standard mistake.

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake