JEE Mains · Maths · STD 11 - 13. statistics
The mean and variance of \(n\) observations are \(8\) and \(16\), respectively. If the sum of the first \((n-1)\) observations is \(48\) and the sum of squares of the first \((n-1)\) observations is \(496\), then the value of \(n\) is:
- A \(21\)
- B \(16\)
- C \(13\)
- D \(7\)
Answer & Solution
Correct Answer
(D) \(7\)
Step-by-step Solution
Detailed explanation
Let the \(n\)-th observation be \(x_n\). Given mean \(\bar{x} = 8\), we have: \(\dfrac{\sum_{i=1}^{n-1} x_i + x_n}{n} = 8\) \(\dfrac{48 + x_n}{n} = 8 \Rightarrow x_n = 8n - 48\) Given variance \(\sigma^2 = 16\), we have:…
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