JEE Mains · Maths · STD 11 - 13. statistics
Consider \(10\) observation \(\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}\). such that \(\sum_{i=1}^{10}\left(x_i-\alpha\right)=2\) and \(\sum_{i=1}^{10}\left(x_i-\beta\right)^2=40\), where \(\alpha, \beta\) are positive integers. Let the mean and the variance of the observations be \(\frac{6}{5}\) and \(\frac{84}{25}\) respectively. The \(\frac{\beta}{\alpha}\) is equal to :
- A \(2\)
- B \(\frac{3}{2}\)
- C \(\frac{5}{2}\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\( \mathrm{x}_1, \mathrm{x}_2 \ldots \ldots . \mathrm{x}_{10} \) \( \sum_{\mathrm{i}=1}^{10}\left(\mathrm{x}_{\mathrm{i}}-\alpha\right)=2 \Rightarrow \sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}-10 \alpha=2 \)…
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