JEE Mains · Maths · STD 11 - 13. statistics
If the mean and the variance of \(6,4, a, 8, b, 12,10\), 13 are 9 and 9.25 respectively, then \(a+b+a b\) is equal to :
- A \(105\)
- B \(103\)
- C \(100\)
- D \(106\)
Answer & Solution
Correct Answer
(B) \(103\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \because \text { mean }=9 \\ & \therefore 53+\mathrm{a}+\mathrm{b}=72 \\ & \Rightarrow \mathrm{a}+\mathrm{b}=19 \\ & \because \sigma^2=\frac{37}{4} \text { and }(\overline{\mathrm{X}})^2+\sigma^2=\frac{\sum \mathrm{x}_1^2}{\mathrm{~N}} \\ & \Rightarrow…
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