JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of a set of \(15\) numbers are \(12\) and \(14\) respectively. The mean and variance of another set of \(15\) numbers are \(14\) and \(\sigma^2\) respectively. If the variance of all the \(30\) numbers in the two sets is \(13\),then \(\sigma^2\) is equal to \(.........\).
- A \(9\)
- B \(12\)
- C \(11\)
- D \(10\)
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
\(\text { Combine var. }=\frac{ n _1 \sigma^2+ n _2 \sigma^2}{ n _1+ n _2}+\frac{ n _1 n _2\left( m _1- m _2\right)^2}{\left( n _1+ n _2\right)^2}\) \(13=\frac{15.14+15 \cdot \sigma^2}{30}+\frac{15.15(12-14)^2}{30 \times 30}\) \(13=\frac{14+\sigma^2}{2}+\frac{4}{4}\)…
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