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For two data sets, each of size 5 , the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 , respectively. The variance of the combined data set is

Options

  1. A11 2
  2. B6
  3. C13 2
  4. D5 2

Correct answer

A. 11 2

Step-by-step solution

_x^2=4 _y^2=5 x =2 y =4 aligned x_i 5 & =2 _x^2 & = ( 1 2 x_i^2 )-( x )^2= 1 5 ( y_i^2 )-16 x_i^2 & =40 y_i^2 & =105 _z^2 & = 1 10 ( x_i^2+ y_i^2 )- ( x + y 2 )^2= 1 10 (40+105)-9= 145-90 10 = 55 10 = 11 2 aligned

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