Questions
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 then the standard deviation of second group is
detailed solution
Correct option is A
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).Similar Questions
For (2n + 1) observations , and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?
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