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Seven real numbers 9 = x1 < x2 <... < x7 form an arithmetic progression with common difference d. If their standard deviation is 4 and their mean is x_bar, find the value of x_bar + x6.

1. 18(1 + 1/sqrt(3))
2. 34
3. 2(9 + 8/sqrt(7))
4. 25

Correct answer: 34

Solution

With n = 7, SD = |d|*sqrt(48/12) = 2|d| = 4, giving d = 2. The mean is the middle term x4 = 9 + 3d = 15, and x6 = 9 + 5d = 19, so x_bar + x6 = 15 + 19 = 34.

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