JEE Mains · Maths · STD 11 - 13. statistics
Let the mean and the variance of \(20\) observations \(x_{1}, x_{2}, \ldots x_{20}\) be \(15\) and \(9 ,\) respectively. For \(\alpha \in R\), if the mean of \(\left( x _{1}+\alpha\right)^{2},\left( x _{2}+\alpha\right)^{2}, \ldots,\left( x _{20}+\alpha\right)^{2}\) is \(178 ,\) then the square of the maximum value of \(\alpha\) is equal to \(...........\)
- A \(0\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(\sum x_{1}=15 \times 20=300 \quad \ldots(i)\) \(\frac{\sum x_{1}^{2}}{20}-(15)^{2}=9\) \(\sum x_{1}^{2}=234 \times 20=4680\) \(\frac{\sum\left(x_{1}+\alpha\right)^{2}}{20}=178 \Rightarrow \sum\left(x_{1}+\alpha\right)^{2}=3560\)…
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