A group of 10 observations has mean 5 and S.D. $\displaystyle 2\sqrt{6}.$ Another group of 20 observations has mean 5 and S.D. $\displaystyle 3\sqrt{2},$ then the S.D. of combined group of 30 observations is
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$\displaystyle \sqrt{5}$
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$\displaystyle 2\sqrt{5}$
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$\displaystyle 3\sqrt{5}$
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None of these
B
Correct answer
Explanation
Combined mean = (10*5 + 20*5) / 30 = 5. Combined variance = (n1(s1^2 + d1^2) + n2(s2^2 + d2^2)) / (n1+n2), where d1 = mean1 - combined_mean = 0. Variance = (10*(24) + 20*(18)) / 30 = (240 + 360) / 30 = 600 / 30 = 20. SD = sqrt(20) = 2*sqrt(5).