JEE Mains · Maths · STD 11 - 13. statistics
Let \(a, b \in R\). Let the mean and the variance of \(6\) observations \(-3,4,7,-6\), \(a,\ b\) be \(2\) and \(23\) , respectively. The mean deviation about the mean of these \(6\) observations is :
- A \(\frac{13}{3}\)
- B \(\frac{16}{3}\)
- C \(\frac{11}{3}\)
- D \(\frac{14}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{13}{3}\)
Step-by-step Solution
Detailed explanation
\( \frac{\sum x_i}{6}=2 \text { and } \frac{\sum x_i^2}{N}-\mu^2=23 \) \( \alpha+\beta=10 \) \( \alpha^2+\beta^2=52\) solving we get \(\alpha=4, \beta=6\) \(\frac{\sum\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{6}=\frac{5+2+5+8+2+4}{6}=\frac{13}{3}\)
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