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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 $SD = \sqrt{13.44}$ , the SD of the second group is

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Correct option is A

We know ,σ2=n1σ12+d12+n2σ22+d22n1+n2where d1=m1−a,d2=m2−a,a being the mean of the whole group.∴ 15.6=100×15+150×m2250⇒m2=16 Thus, 13.44=100×9+150×σ2+100×(0.6)2+150×(0.4)2250⇒σ=4

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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

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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 $SD = \sqrt{13.44}$ , the SD of the second group is