ExamBro
ExamBro
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:

  1. A 12
  2. B 14
  3. C 16
  4. D 20
Verified Solution

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…