JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of \(8\) observations are \(10\) and \(13.5,\) respectively. If \(6\) of these observations are \(5,7,10,12,14,15,\) then the absolute difference of the remaining two observations is
- A \(7\)
- B \(3\)
- C \(5\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(7\)
Step-by-step Solution
Detailed explanation
\(\bar{x}=10\) \(\Rightarrow \bar{x}=\frac{63+a+b}{8}=10 \Rightarrow a+b=17\) since, variance is independent of origin. So, we subtract 10 from each observation. \(So , \sigma^{2}=13.5=\frac{79+( a -10)^{2}+( b -10)^{2}}{8}-(10-10)^{2}\)…
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