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For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

1. 11/2
2. 6
3. 13/2
4. 5/2

Correct answer: 11/2

Solution

Equal sizes give grand mean = 3. Deviations of group means: -1 and +1. Combined variance = [5(4+1) + 5(5+1)] / 10 = (25 + 30)/10 = 55/10 = 11/2.

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