JEE Mains · Maths · STD 11 - 13. statistics
Let \( X=\{x\in\mathbb{N}:1\le x\le19\} \) and for some \( a, b\in\mathbb{R}, Y=\{ax+b:x\in X\}. \) If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is
- A 20
- B 80
- C 100
- D 60
Answer & Solution
Correct Answer
(D) 60
Step-by-step Solution
Detailed explanation
\(\Sigma y_{i}=a \Sigma x_{i}+\Sigma b\) \(=a \times(1+2+\ldots+19)+19 b\) \(\frac{\Sigma y_{i}}{19}=\frac{a \times 19 \times 20}{2 \times 19}+b\) \(30=10 a+b \quad\ldots(1)\) Variance of \(X =\frac{\Sigma x _{ i }^2}{19}-\left(\frac{\Sigma x _{ i }}{19}\right)^2\)…
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