A set of four observations has mean 1 and…

Single correct+4 / -1Answer matches NTA’s final key

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to:

5.96
6.14
6.04
6.24

Solution

Work with sums: for each set, $\sum x^2 = n(\sigma^2 + \bar x^2)$ .

First set: $\sum x = 4$ , $\sum x^2 = 4(13 + 1) = 56$ .
Second set: $\sum x = 12$ , $\sum x^2 = 6(1 + 4) = 30$ .

Combined: mean $= \frac{16}{10} = 1.6$ and

$\sigma^2 = \frac{56 + 30}{10} - 1.6^2 = 8.6 - 2.56 = 6.04.$

Answer: 6.04.

Answer checked against the official answer key. The solution is our own working.

JEE MAIN 2026 · Statistics and Probability

Solution

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