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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.

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. Correct Answer 26.17

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 = /650 = 26.17.

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