JEE Mains · Maths · STD 11 - 13. statistics
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:
- A \(5.96\)
- B \(6.14\)
- C \(6.04\)
- D \(6.24\)
Answer & Solution
Correct Answer
(C) \(6.04\)
Step-by-step Solution
Detailed explanation
Given for the first set: \(n_1 = 4\), \(\bar{x}_1 = 1\), \(\sigma_1^2 = 13\). \(\sigma_1^2 = \dfrac{\sum x_i^2}{n_1} - (\bar{x}_1)^2\) \(13 = \dfrac{\sum x_i^2}{4} - 1^2 \Rightarrow \sum x_i^2 = 56\) Also, \(\sum x_i = n_1 \bar{x}_1 = 4 \times 1 = 4\) Given for the second set:…
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