For two data sets, each of size 5, the variance 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

For two data sets, each of size 5, the variance 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

  1. A

    52

  2. B

    112

  3. C

    6

  4. D

    `132

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    Solution:

    σx2=4 and σy2=5

    Also, x¯=2 and y¯=4

    now,Σxi5=2Σxi=10;Σyi=20and σx2=15Σxi2(x¯)2Σxi2=5(4+4)Σxi2=40and σ2y=15Σyi2(y¯)2and Σyi2=5(5+16)Σyi2=105 

    combined mean, 

    σz2=110Σxi2+Σyi2x¯+y¯22=110(40+105)9=1459010=5510=112

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