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AP EAMCET · Maths · Statistics

For the set \(A=\left\{x_1, x_2, x_3, x_4, x_5\right\}\) the variance is 4 and the mean is 2 . For the set \(B=0\left\{y_1, y_2, y_3, y_4, y_5\right\}\) the variance is 5 and the mean is 4 . Then, the variance of \(A \cup B\) is

  1. A 6
  2. B 6.5
  3. C 5.5
  4. D 5
Verified Solution

Answer & Solution

Correct Answer

(C) 5.5

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { (c) } A=\left\{x_1, x_2, x_3, x_4, x_5\right\} \\ & \text { Mean }=\frac{\Sigma x_i}{5}=2 \Rightarrow \sum_{i=1}^5 x_i=10 \\ & \text { Variance, } \frac{1}{5-1}\left[\Sigma x_i^2-\frac{\left(\Sigma x_i\right)^2}{5}\right]=4 \\ & =\frac{1}{4}\left[\Sigma…