JEE Mains · Maths · STD 11 - 13. statistics
If the mean and variance of the frequency distribution
| \(x_i\) | \(2\) | \(4\) | \(6\) | \(8\) | \(10\) | \(12\) | \(14\) | \(16\) |
| \(f_i\) | \(4\) | \(4\) | \(\alpha\) | \(15\) | \(8\) | \(\beta\) | \(4\) | \(5\) |
- A \(24\)
- B \(23\)
- C \(25\)
- D \(22\)
Answer & Solution
Correct Answer
(C) \(25\)
Step-by-step Solution
Detailed explanation
\(N=\sum f_i=40+\alpha+\beta\) \(\sum f_i x_i=360+6 \alpha+12 \beta\) \(\sum f _{ i } x _{ i }^2=3904+36 \alpha+144 \beta\) \(\operatorname{Mean}(\overline{ x })=\frac{\sum f _{ i } x _{ i }}{\sum f _{ i }}=9\) \(\Rightarrow 360+6 \alpha+12 \beta=9(40+\alpha+\beta)\)…
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