For two data sets, each with size 5, the variances are given to be 3 and 4 and the corresponding means are given to be 2 and 4, respectively. The…

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For two data sets, each with size 5, the variances are given to be 3 and 4 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

MARKS Content Team · Accepted Answer

Correct answer: (B) 9/2. σx2=3 σy2=4 x ¯ =2 y ¯ =4 (Σx_i)/5=2⇒Σx_i=10;Σy_i=20; σ x 2 = 1/5 ∑ x i 2 −x ¯^2 ⇒1/5 ∑ x i 2 −4=3 ∑xi2=35 ∑yi2=100 σ z 2 =1/10 ∑ x i 2 +∑ y i 2 −x ¯ + y ¯^(2 2) =1/1035+100-9=(135-90)/10 =45/10=9/2

For two data sets, each with size $5,$ the variances are given to be $3$ and $4$ and the corresponding means are given to be $2$ and $4,$ respectively. The variance of the combined data set is

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