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The mean of two samples of the sizes 250 and 320 were found to be 20,12 respectively. Their standard deviations were 2 & 5, respectively. Find the variance of combined sample of size 650.(a) 10.23(b) 32.5(c) 65(d) 26.17I got this question in an internship interview.This interesting question is from Statistics topic in portion Statistics of Mathematics – Class 11

Answer»

The correct answer is (d) 26.17

Explanation: COMBINED Mean = X = (n1x1 + n2x2)/(n1 + N2) = (250 × 20 + 320 × 12)/650 = 13.6

Let d1 = x1 – X = 20-13.6 = 6.4, d2 = x2 – X = 12-13.6 = -1.6

Variance = [250(6.4 + 40.96) + 320(13.6 + 2.56)]/650 = 26.17.



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