Multiple choice

Two sets of data consisting of 10 and 20 observations have same mean 8 with standard deviations of 1 and 2, respectively. If the two data sets are combined, then the variance is:

  1. 3

  2. 2

  3. 5

  4. 1.5
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A Correct answer
Explanation

Combined mean is 8. Combined variance is calculated using the formula for pooled variance: (n1*v1 + n2*v2 + n1*d1^2 + n2*d2^2) / (n1 + n2). Since both means are 8, d1=0 and d2=0. Thus, (10*1 + 20*4) / 30 = 90 / 30 = 3.

AI explanation

The combined mean is calculated as (10 times 8 + 20 times 8) / 30, which equals 8. Using the formula for combined variance, we calculate n1 times (sigma1 squared + d1 squared) + n2 times (sigma2 squared + d2 squared) divided by N, where d1 and d2 are 8 minus 8, making them zero. The combined variance is (10 times (1 squared + 0) + 20 times (2 squared + 0)) / 30, equaling (10 + 80) / 30. This results in a combined variance of 3.

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