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Question

For two data sets X and Y, each of size 5, the means are given to be 2 and 4 and the corresponding variances are 4 and 5, respectively. The variance of the combined data set is
(correct answer + 1, wrong answer - 0.25)

A
5.5
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B
5.6
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C
4.5
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D
4.8
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Solution

The correct option is A 5.5
Given, ¯¯¯x=2 and ¯¯¯y=4
xi=2×5=10 and yi=4×5=20

Also, σ2x=4 and σ2y=5
15x2i(2)2=4 and 15y2i(4)2=5
x2i=40 and y2i=105

Combined variance
=15+5(x2i+y2i)(xi+yi5+5)2
=110(40+105)(10+2010)2
=14.59
=5.5

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