AP EAMCET · Maths · Statistics
If \(x_1, x_2, x_3 \ldots x_n\) are \(n\) observations such that \(\Sigma\left(x_i+2\right)^2=28 n\) and \(\Sigma\left(x_i-2\right)^2=12 n\), then the variance is:
- A 12
- B 14
- C 16
- D 20
Answer & Solution
Correct Answer
(A) 12
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given that } \sum\left(x_i+2\right)^2=28 n \\ & \Rightarrow \sum x_i^2+4 \sum x_i+4 n=28 n \\ & \Rightarrow \sum x_i^2+4 \sum x_i=24 n ....(i)\end{aligned}\) Similarly \(\sum\left(x_i-2\right)^2=12 n \Rightarrow \sum x_i^2-4 \sum x_i=8 n\) On solving…
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