55, 60, 61, 63, 64, 65, 66, 70 Mean = 63 S.d = 4.133 M.a.d = 3.25 The question is asking to find a new set of values where the mean is 65 and the m.a.d has doubled. How would I go about doing this?
We need a set of numbers whose mean is 65 and whose m.a.d. (mean absolute deviation) is 6.5.
Suppose the set has 8 numbers. Then the sum of the absolute values of the differences of the values and 65 is eight times 6.5 or 52. Then we could let half of the numbers be 52/8=6.5 below 65, and half the numbers be 6.5 above the mean.
The set would be 58.5,58.5,58.5,58.5,71.5,71.5,71.5,71.5
The mean is clearly 65.
The m.a.d. is (4|58.5-65|+4|71.5-65|)/8 = 52/8=6.5 as required.
If there are other restrictions (such as the numbers must be uniques, or integers, etc...) we can find another set.
For example, with 8 numbers we could use 55,57,60,62,68,70,73,75. Note that the total distance from 65 is 52 -- 26 below and 26 above.