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

Question

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

Infinity Learn · Accepted Answer

Given that $$n1=100$$,$$x1$$¯$$=15$$,σ$$1=3$$,$$n2=150n=n1+n2=250$$,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 σ$$2=1n1+n2n1$$σ$$12+d12+n2$$σ$$22+d22$$⇒(13.44)2=125010032+($$−$$0.6)2+150$$σ$$22+(0.4)2$$∴σ$$2=4Therefore$$, the correct answer is $$(1).

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 $\sqrt{13.44}$ then the standard deviation of second group is

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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

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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 $\sqrt{13.44}$ then the standard deviation of second group is