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One series of 5 observations has mean 8 and variance 24, and a second series of 3 observations also has mean 8 and variance 24. Find the variance of the combined series of 8 observations.

1. 20
2. 24
3. 25
4. 42

Correct answer: 24

Solution

Since both groups have mean 8, the deviation terms vanish and the combined variance is just the weighted average of the equal variances, which is 24.

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