The first group of two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation  13.44 then the standard deviation  of second group is

Given that n1=100,x1¯=15,σ1=3,n2=150n=n1+n2=250,x¯=15.6,σ=13.44 Further x¯=n1x¯1+n2x¯2n1+n2⇒15.6=100(15)+150x¯2250⇒x¯2=16d1=x¯1−x¯=15−15.6=−0.6,d2=x¯2−x¯=16−15.6=0.4 We know that σ2=1n1+n2n1σ12+d12+n2σ22+d22⇒(13.44)2=125010032+(−0.6)2+150σ22+(0.4)2∴σ2=4Therefore, the correct answer is (1).