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If the mean deviation of the numbers 1, 1 + d, 1 + 2d,..., 1 + 100d from their mean is 255, then d is equal to:

1. 20.0
2. 10.1
3. 20.2
4. 10.0

Correct answer: 10.1

Solution

Mean = 1+50d. Mean deviation = d*(sum_{k=0}^{100}|k-50|)/101 = d*2550/101. Setting equal to 255 gives d=10.1.

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