The first of two samples has 100 items with mean 15 and SD = 3. If the whole group has 250 items with mean 15.6 and SD=13.44, the SD of the second group is

The first of two samples has 100 items with mean 15 and SD = 3. If the whole group has 250 items with mean 15.6 and SD=13.44, the SD of the second group is

  1. A

    4

  2. B

    5

  3. C

    6

  4. D

    3.52

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    Solution:

    We know ,σ2=n1σ12+d12+n2σ22+d22n1+n2

    where d1=m1a,d2=m2a,a  being the mean of the whole group.

     15.6=100×15+150×m2250m2=16 Thus,  13.44=100×9+150×σ2+100×(0.6)2+150×(0.4)2250σ=4

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