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The mean and standard deviation of 10 observations are 20 and 2 respectively. Each observation is first multiplied by p (p not 0) and then q (q not 0) is subtracted. If both the new mean and the new standard deviation are half their original values, what is the value of q?

1. -20
2. 10
3. -10
4. -5

Correct answer: -20

Solution

The new SD must be half the old SD: |p| * 2 = 1 so |p| = 1/2. Since the new mean must also be positive (10, half of 20), trying p = -1/2 gives new mean = -10 - q = 10, so q = -20. With p = +1/2 we get q = 0 which is not allowed.

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