Open Middle®
Directions: Construct two sets of 9 numbers that have a mean of 6 and and MAD (mean absolute deviation) of 2.
Hint
How could you create a set of data has a mean of 6?
Without changing the mean, how could you adjust the data set to get a MAD of 2?
Without changing the mean, how could you adjust the data set to get a MAD of 2?
Answer
There are multiple answers to this problem especially if you change the domain from whole numbers to integers to rational numbers. The only constraints on a solution is the sum of the set of data must be 54 and the total absolute deviation (TAD) must be 18. One example is 3,3,3,6,6,6,9,9,9
Source: Patrick Sullivan
My answer is 666333999.
my answer is 333,666,999
9,9,9,3,3,3,6,6,6
3,3,3,6,6,6,9,9,9
mine is 3,3,3,6,6,6,9,9,9
In the non-negative integers, there are 487 solutions (410 in the positive integers) and all of them have at least one repeat number. In the integers and the rational numbers, there are infinitely many solutions.
[0, 3, 6, 6, 6, 6, 6, 6, 15]
[0, 3, 6, 6, 6, 6, 6, 7, 14]
[0, 3, 6, 6, 6, 6, 6, 8, 13]
[0, 3, 6, 6, 6, 6, 6, 9, 12]
[0, 3, 6, 6, 6, 6, 6, 10, 11]
[0, 3, 6, 6, 6, 6, 7, 7, 13]
[0, 3, 6, 6, 6, 6, 7, 8, 12]
[0, 3, 6, 6, 6, 6, 7, 9, 11]
[0, 3, 6, 6, 6, 6, 7, 10, 10]
[0, 3, 6, 6, 6, 6, 8, 8, 11]
[0, 3, 6, 6, 6, 6, 8, 9, 10]
[0, 3, 6, 6, 6, 6, 9, 9, 9]
[0, 3, 6, 6, 6, 7, 7, 7, 12]
[0, 3, 6, 6, 6, 7, 7, 8, 11]
[0, 3, 6, 6, 6, 7, 7, 9, 10]
[0, 3, 6, 6, 6, 7, 8, 8, 10]
[0, 3, 6, 6, 6, 7, 8, 9, 9]
[0, 3, 6, 6, 6, 8, 8, 8, 9]
[0, 3, 6, 6, 7, 7, 7, 7, 11]
[0, 3, 6, 6, 7, 7, 7, 8, 10]
[0, 3, 6, 6, 7, 7, 7, 9, 9]
[0, 3, 6, 6, 7, 7, 8, 8, 9]
[0, 3, 6, 6, 7, 8, 8, 8, 8]
[0, 3, 6, 7, 7, 7, 7, 7, 10]
[0, 3, 6, 7, 7, 7, 7, 8, 9]
[0, 3, 6, 7, 7, 7, 8, 8, 8]
[0, 3, 7, 7, 7, 7, 7, 7, 9]
[0, 3, 7, 7, 7, 7, 7, 8, 8]
[0, 4, 5, 6, 6, 6, 6, 6, 15]
[0, 4, 5, 6, 6, 6, 6, 7, 14]
[0, 4, 5, 6, 6, 6, 6, 8, 13]
[0, 4, 5, 6, 6, 6, 6, 9, 12]
[0, 4, 5, 6, 6, 6, 6, 10, 11]
[0, 4, 5, 6, 6, 6, 7, 7, 13]
[0, 4, 5, 6, 6, 6, 7, 8, 12]
[0, 4, 5, 6, 6, 6, 7, 9, 11]
[0, 4, 5, 6, 6, 6, 7, 10, 10]
[0, 4, 5, 6, 6, 6, 8, 8, 11]
[0, 4, 5, 6, 6, 6, 8, 9, 10]
[0, 4, 5, 6, 6, 6, 9, 9, 9]
[0, 4, 5, 6, 6, 7, 7, 7, 12]
[0, 4, 5, 6, 6, 7, 7, 8, 11]
[0, 4, 5, 6, 6, 7, 7, 9, 10]
[0, 4, 5, 6, 6, 7, 8, 8, 10]
[0, 4, 5, 6, 6, 7, 8, 9, 9]
[0, 4, 5, 6, 6, 8, 8, 8, 9]
[0, 4, 5, 6, 7, 7, 7, 7, 11]
[0, 4, 5, 6, 7, 7, 7, 8, 10]
[0, 4, 5, 6, 7, 7, 7, 9, 9]
[0, 4, 5, 6, 7, 7, 8, 8, 9]
[0, 4, 5, 6, 7, 8, 8, 8, 8]
[0, 4, 5, 7, 7, 7, 7, 7, 10]
[0, 4, 5, 7, 7, 7, 7, 8, 9]
[0, 4, 5, 7, 7, 7, 8, 8, 8]
[0, 5, 5, 5, 6, 6, 6, 6, 15]
[0, 5, 5, 5, 6, 6, 6, 7, 14]
[0, 5, 5, 5, 6, 6, 6, 8, 13]
[0, 5, 5, 5, 6, 6, 6, 9, 12]
[0, 5, 5, 5, 6, 6, 6, 10, 11]
[0, 5, 5, 5, 6, 6, 7, 7, 13]
[0, 5, 5, 5, 6, 6, 7, 8, 12]
[0, 5, 5, 5, 6, 6, 7, 9, 11]
[0, 5, 5, 5, 6, 6, 7, 10, 10]
[0, 5, 5, 5, 6, 6, 8, 8, 11]
[0, 5, 5, 5, 6, 6, 8, 9, 10]
[0, 5, 5, 5, 6, 6, 9, 9, 9]
[0, 5, 5, 5, 6, 7, 7, 7, 12]
[0, 5, 5, 5, 6, 7, 7, 8, 11]
[0, 5, 5, 5, 6, 7, 7, 9, 10]
[0, 5, 5, 5, 6, 7, 8, 8, 10]
[0, 5, 5, 5, 6, 7, 8, 9, 9]
[0, 5, 5, 5, 6, 8, 8, 8, 9]
[0, 5, 5, 5, 7, 7, 7, 7, 11]
[0, 5, 5, 5, 7, 7, 7, 8, 10]
[0, 5, 5, 5, 7, 7, 7, 9, 9]
[0, 5, 5, 5, 7, 7, 8, 8, 9]
[0, 5, 5, 5, 7, 8, 8, 8, 8]
[1, 2, 6, 6, 6, 6, 6, 6, 15]
[1, 2, 6, 6, 6, 6, 6, 7, 14]
[1, 2, 6, 6, 6, 6, 6, 8, 13]
[1, 2, 6, 6, 6, 6, 6, 9, 12]
[1, 2, 6, 6, 6, 6, 6, 10, 11]
[1, 2, 6, 6, 6, 6, 7, 7, 13]
[1, 2, 6, 6, 6, 6, 7, 8, 12]
[1, 2, 6, 6, 6, 6, 7, 9, 11]
[1, 2, 6, 6, 6, 6, 7, 10, 10]
[1, 2, 6, 6, 6, 6, 8, 8, 11]
[1, 2, 6, 6, 6, 6, 8, 9, 10]
[1, 2, 6, 6, 6, 6, 9, 9, 9]
[1, 2, 6, 6, 6, 7, 7, 7, 12]
[1, 2, 6, 6, 6, 7, 7, 8, 11]
[1, 2, 6, 6, 6, 7, 7, 9, 10]
[1, 2, 6, 6, 6, 7, 8, 8, 10]
[1, 2, 6, 6, 6, 7, 8, 9, 9]
[1, 2, 6, 6, 6, 8, 8, 8, 9]
[1, 2, 6, 6, 7, 7, 7, 7, 11]
[1, 2, 6, 6, 7, 7, 7, 8, 10]
[1, 2, 6, 6, 7, 7, 7, 9, 9]
[1, 2, 6, 6, 7, 7, 8, 8, 9]
[1, 2, 6, 6, 7, 8, 8, 8, 8]
[1, 2, 6, 7, 7, 7, 7, 7, 10]
[1, 2, 6, 7, 7, 7, 7, 8, 9]
[1, 2, 6, 7, 7, 7, 8, 8, 8]
[1, 2, 7, 7, 7, 7, 7, 7, 9]
[1, 2, 7, 7, 7, 7, 7, 8, 8]
[1, 3, 5, 6, 6, 6, 6, 6, 15]
[1, 3, 5, 6, 6, 6, 6, 7, 14]
[1, 3, 5, 6, 6, 6, 6, 8, 13]
[1, 3, 5, 6, 6, 6, 6, 9, 12]
[1, 3, 5, 6, 6, 6, 6, 10, 11]
[1, 3, 5, 6, 6, 6, 7, 7, 13]
[1, 3, 5, 6, 6, 6, 7, 8, 12]
[1, 3, 5, 6, 6, 6, 7, 9, 11]
[1, 3, 5, 6, 6, 6, 7, 10, 10]
[1, 3, 5, 6, 6, 6, 8, 8, 11]
[1, 3, 5, 6, 6, 6, 8, 9, 10]
[1, 3, 5, 6, 6, 6, 9, 9, 9]
[1, 3, 5, 6, 6, 7, 7, 7, 12]
[1, 3, 5, 6, 6, 7, 7, 8, 11]
[1, 3, 5, 6, 6, 7, 7, 9, 10]
[1, 3, 5, 6, 6, 7, 8, 8, 10]
[1, 3, 5, 6, 6, 7, 8, 9, 9]
[1, 3, 5, 6, 6, 8, 8, 8, 9]
[1, 3, 5, 6, 7, 7, 7, 7, 11]
[1, 3, 5, 6, 7, 7, 7, 8, 10]
[1, 3, 5, 6, 7, 7, 7, 9, 9]
[1, 3, 5, 6, 7, 7, 8, 8, 9]
[1, 3, 5, 6, 7, 8, 8, 8, 8]
[1, 3, 5, 7, 7, 7, 7, 7, 10]
[1, 3, 5, 7, 7, 7, 7, 8, 9]
[1, 3, 5, 7, 7, 7, 8, 8, 8]
[1, 4, 4, 6, 6, 6, 6, 6, 15]
[1, 4, 4, 6, 6, 6, 6, 7, 14]
[1, 4, 4, 6, 6, 6, 6, 8, 13]
[1, 4, 4, 6, 6, 6, 6, 9, 12]
[1, 4, 4, 6, 6, 6, 6, 10, 11]
[1, 4, 4, 6, 6, 6, 7, 7, 13]
[1, 4, 4, 6, 6, 6, 7, 8, 12]
[1, 4, 4, 6, 6, 6, 7, 9, 11]
[1, 4, 4, 6, 6, 6, 7, 10, 10]
[1, 4, 4, 6, 6, 6, 8, 8, 11]
[1, 4, 4, 6, 6, 6, 8, 9, 10]
[1, 4, 4, 6, 6, 6, 9, 9, 9]
[1, 4, 4, 6, 6, 7, 7, 7, 12]
[1, 4, 4, 6, 6, 7, 7, 8, 11]
[1, 4, 4, 6, 6, 7, 7, 9, 10]
[1, 4, 4, 6, 6, 7, 8, 8, 10]
[1, 4, 4, 6, 6, 7, 8, 9, 9]
[1, 4, 4, 6, 6, 8, 8, 8, 9]
[1, 4, 4, 6, 7, 7, 7, 7, 11]
[1, 4, 4, 6, 7, 7, 7, 8, 10]
[1, 4, 4, 6, 7, 7, 7, 9, 9]
[1, 4, 4, 6, 7, 7, 8, 8, 9]
[1, 4, 4, 6, 7, 8, 8, 8, 8]
[1, 4, 4, 7, 7, 7, 7, 7, 10]
[1, 4, 4, 7, 7, 7, 7, 8, 9]
[1, 4, 4, 7, 7, 7, 8, 8, 8]
[1, 4, 5, 5, 6, 6, 6, 6, 15]
[1, 4, 5, 5, 6, 6, 6, 7, 14]
[1, 4, 5, 5, 6, 6, 6, 8, 13]
[1, 4, 5, 5, 6, 6, 6, 9, 12]
[1, 4, 5, 5, 6, 6, 6, 10, 11]
[1, 4, 5, 5, 6, 6, 7, 7, 13]
[1, 4, 5, 5, 6, 6, 7, 8, 12]
[1, 4, 5, 5, 6, 6, 7, 9, 11]
[1, 4, 5, 5, 6, 6, 7, 10, 10]
[1, 4, 5, 5, 6, 6, 8, 8, 11]
[1, 4, 5, 5, 6, 6, 8, 9, 10]
[1, 4, 5, 5, 6, 6, 9, 9, 9]
[1, 4, 5, 5, 6, 7, 7, 7, 12]
[1, 4, 5, 5, 6, 7, 7, 8, 11]
[1, 4, 5, 5, 6, 7, 7, 9, 10]
[1, 4, 5, 5, 6, 7, 8, 8, 10]
[1, 4, 5, 5, 6, 7, 8, 9, 9]
[1, 4, 5, 5, 6, 8, 8, 8, 9]
[1, 4, 5, 5, 7, 7, 7, 7, 11]
[1, 4, 5, 5, 7, 7, 7, 8, 10]
[1, 4, 5, 5, 7, 7, 7, 9, 9]
[1, 4, 5, 5, 7, 7, 8, 8, 9]
[1, 4, 5, 5, 7, 8, 8, 8, 8]
[1, 5, 5, 5, 5, 6, 6, 6, 15]
[1, 5, 5, 5, 5, 6, 6, 7, 14]
[1, 5, 5, 5, 5, 6, 6, 8, 13]
[1, 5, 5, 5, 5, 6, 6, 9, 12]
[1, 5, 5, 5, 5, 6, 6, 10, 11]
[1, 5, 5, 5, 5, 6, 7, 7, 13]
[1, 5, 5, 5, 5, 6, 7, 8, 12]
[1, 5, 5, 5, 5, 6, 7, 9, 11]
[1, 5, 5, 5, 5, 6, 7, 10, 10]
[1, 5, 5, 5, 5, 6, 8, 8, 11]
[1, 5, 5, 5, 5, 6, 8, 9, 10]
[1, 5, 5, 5, 5, 6, 9, 9, 9]
[1, 5, 5, 5, 5, 7, 7, 7, 12]
[1, 5, 5, 5, 5, 7, 7, 8, 11]
[1, 5, 5, 5, 5, 7, 7, 9, 10]
[1, 5, 5, 5, 5, 7, 8, 8, 10]
[1, 5, 5, 5, 5, 7, 8, 9, 9]
[1, 5, 5, 5, 5, 8, 8, 8, 9]
[2, 2, 5, 6, 6, 6, 6, 6, 15]
[2, 2, 5, 6, 6, 6, 6, 7, 14]
[2, 2, 5, 6, 6, 6, 6, 8, 13]
[2, 2, 5, 6, 6, 6, 6, 9, 12]
[2, 2, 5, 6, 6, 6, 6, 10, 11]
[2, 2, 5, 6, 6, 6, 7, 7, 13]
[2, 2, 5, 6, 6, 6, 7, 8, 12]
[2, 2, 5, 6, 6, 6, 7, 9, 11]
[2, 2, 5, 6, 6, 6, 7, 10, 10]
[2, 2, 5, 6, 6, 6, 8, 8, 11]
[2, 2, 5, 6, 6, 6, 8, 9, 10]
[2, 2, 5, 6, 6, 6, 9, 9, 9]
[2, 2, 5, 6, 6, 7, 7, 7, 12]
[2, 2, 5, 6, 6, 7, 7, 8, 11]
[2, 2, 5, 6, 6, 7, 7, 9, 10]
[2, 2, 5, 6, 6, 7, 8, 8, 10]
[2, 2, 5, 6, 6, 7, 8, 9, 9]
[2, 2, 5, 6, 6, 8, 8, 8, 9]
[2, 2, 5, 6, 7, 7, 7, 7, 11]
[2, 2, 5, 6, 7, 7, 7, 8, 10]
[2, 2, 5, 6, 7, 7, 7, 9, 9]
[2, 2, 5, 6, 7, 7, 8, 8, 9]
[2, 2, 5, 6, 7, 8, 8, 8, 8]
[2, 2, 5, 7, 7, 7, 7, 7, 10]
[2, 2, 5, 7, 7, 7, 7, 8, 9]
[2, 2, 5, 7, 7, 7, 8, 8, 8]
[2, 3, 4, 6, 6, 6, 6, 6, 15]
[2, 3, 4, 6, 6, 6, 6, 7, 14]
[2, 3, 4, 6, 6, 6, 6, 8, 13]
[2, 3, 4, 6, 6, 6, 6, 9, 12]
[2, 3, 4, 6, 6, 6, 6, 10, 11]
[2, 3, 4, 6, 6, 6, 7, 7, 13]
[2, 3, 4, 6, 6, 6, 7, 8, 12]
[2, 3, 4, 6, 6, 6, 7, 9, 11]
[2, 3, 4, 6, 6, 6, 7, 10, 10]
[2, 3, 4, 6, 6, 6, 8, 8, 11]
[2, 3, 4, 6, 6, 6, 8, 9, 10]
[2, 3, 4, 6, 6, 6, 9, 9, 9]
[2, 3, 4, 6, 6, 7, 7, 7, 12]
[2, 3, 4, 6, 6, 7, 7, 8, 11]
[2, 3, 4, 6, 6, 7, 7, 9, 10]
[2, 3, 4, 6, 6, 7, 8, 8, 10]
[2, 3, 4, 6, 6, 7, 8, 9, 9]
[2, 3, 4, 6, 6, 8, 8, 8, 9]
[2, 3, 4, 6, 7, 7, 7, 7, 11]
[2, 3, 4, 6, 7, 7, 7, 8, 10]
[2, 3, 4, 6, 7, 7, 7, 9, 9]
[2, 3, 4, 6, 7, 7, 8, 8, 9]
[2, 3, 4, 6, 7, 8, 8, 8, 8]
[2, 3, 4, 7, 7, 7, 7, 7, 10]
[2, 3, 4, 7, 7, 7, 7, 8, 9]
[2, 3, 4, 7, 7, 7, 8, 8, 8]
[2, 3, 5, 5, 6, 6, 6, 6, 15]
[2, 3, 5, 5, 6, 6, 6, 7, 14]
[2, 3, 5, 5, 6, 6, 6, 8, 13]
[2, 3, 5, 5, 6, 6, 6, 9, 12]
[2, 3, 5, 5, 6, 6, 6, 10, 11]
[2, 3, 5, 5, 6, 6, 7, 7, 13]
[2, 3, 5, 5, 6, 6, 7, 8, 12]
[2, 3, 5, 5, 6, 6, 7, 9, 11]
[2, 3, 5, 5, 6, 6, 7, 10, 10]
[2, 3, 5, 5, 6, 6, 8, 8, 11]
[2, 3, 5, 5, 6, 6, 8, 9, 10]
[2, 3, 5, 5, 6, 6, 9, 9, 9]
[2, 3, 5, 5, 6, 7, 7, 7, 12]
[2, 3, 5, 5, 6, 7, 7, 8, 11]
[2, 3, 5, 5, 6, 7, 7, 9, 10]
[2, 3, 5, 5, 6, 7, 8, 8, 10]
[2, 3, 5, 5, 6, 7, 8, 9, 9]
[2, 3, 5, 5, 6, 8, 8, 8, 9]
[2, 3, 5, 5, 7, 7, 7, 7, 11]
[2, 3, 5, 5, 7, 7, 7, 8, 10]
[2, 3, 5, 5, 7, 7, 7, 9, 9]
[2, 3, 5, 5, 7, 7, 8, 8, 9]
[2, 3, 5, 5, 7, 8, 8, 8, 8]
[2, 4, 4, 5, 6, 6, 6, 6, 15]
[2, 4, 4, 5, 6, 6, 6, 7, 14]
[2, 4, 4, 5, 6, 6, 6, 8, 13]
[2, 4, 4, 5, 6, 6, 6, 9, 12]
[2, 4, 4, 5, 6, 6, 6, 10, 11]
[2, 4, 4, 5, 6, 6, 7, 7, 13]
[2, 4, 4, 5, 6, 6, 7, 8, 12]
[2, 4, 4, 5, 6, 6, 7, 9, 11]
[2, 4, 4, 5, 6, 6, 7, 10, 10]
[2, 4, 4, 5, 6, 6, 8, 8, 11]
[2, 4, 4, 5, 6, 6, 8, 9, 10]
[2, 4, 4, 5, 6, 6, 9, 9, 9]
[2, 4, 4, 5, 6, 7, 7, 7, 12]
[2, 4, 4, 5, 6, 7, 7, 8, 11]
[2, 4, 4, 5, 6, 7, 7, 9, 10]
[2, 4, 4, 5, 6, 7, 8, 8, 10]
[2, 4, 4, 5, 6, 7, 8, 9, 9]
[2, 4, 4, 5, 6, 8, 8, 8, 9]
[2, 4, 4, 5, 7, 7, 7, 7, 11]
[2, 4, 4, 5, 7, 7, 7, 8, 10]
[2, 4, 4, 5, 7, 7, 7, 9, 9]
[2, 4, 4, 5, 7, 7, 8, 8, 9]
[2, 4, 4, 5, 7, 8, 8, 8, 8]
[2, 4, 5, 5, 5, 6, 6, 6, 15]
[2, 4, 5, 5, 5, 6, 6, 7, 14]
[2, 4, 5, 5, 5, 6, 6, 8, 13]
[2, 4, 5, 5, 5, 6, 6, 9, 12]
[2, 4, 5, 5, 5, 6, 6, 10, 11]
[2, 4, 5, 5, 5, 6, 7, 7, 13]
[2, 4, 5, 5, 5, 6, 7, 8, 12]
[2, 4, 5, 5, 5, 6, 7, 9, 11]
[2, 4, 5, 5, 5, 6, 7, 10, 10]
[2, 4, 5, 5, 5, 6, 8, 8, 11]
[2, 4, 5, 5, 5, 6, 8, 9, 10]
[2, 4, 5, 5, 5, 6, 9, 9, 9]
[2, 4, 5, 5, 5, 7, 7, 7, 12]
[2, 4, 5, 5, 5, 7, 7, 8, 11]
[2, 4, 5, 5, 5, 7, 7, 9, 10]
[2, 4, 5, 5, 5, 7, 8, 8, 10]
[2, 4, 5, 5, 5, 7, 8, 9, 9]
[2, 4, 5, 5, 5, 8, 8, 8, 9]
[2, 5, 5, 5, 5, 5, 6, 6, 15]
[2, 5, 5, 5, 5, 5, 6, 7, 14]
[2, 5, 5, 5, 5, 5, 6, 8, 13]
[2, 5, 5, 5, 5, 5, 6, 9, 12]
[2, 5, 5, 5, 5, 5, 6, 10, 11]
[2, 5, 5, 5, 5, 5, 7, 7, 13]
[2, 5, 5, 5, 5, 5, 7, 8, 12]
[2, 5, 5, 5, 5, 5, 7, 9, 11]
[2, 5, 5, 5, 5, 5, 7, 10, 10]
[2, 5, 5, 5, 5, 5, 8, 8, 11]
[2, 5, 5, 5, 5, 5, 8, 9, 10]
[2, 5, 5, 5, 5, 5, 9, 9, 9]
[3, 3, 3, 6, 6, 6, 6, 6, 15]
[3, 3, 3, 6, 6, 6, 6, 7, 14]
[3, 3, 3, 6, 6, 6, 6, 8, 13]
[3, 3, 3, 6, 6, 6, 6, 9, 12]
[3, 3, 3, 6, 6, 6, 6, 10, 11]
[3, 3, 3, 6, 6, 6, 7, 7, 13]
[3, 3, 3, 6, 6, 6, 7, 8, 12]
[3, 3, 3, 6, 6, 6, 7, 9, 11]
[3, 3, 3, 6, 6, 6, 7, 10, 10]
[3, 3, 3, 6, 6, 6, 8, 8, 11]
[3, 3, 3, 6, 6, 6, 8, 9, 10]
[3, 3, 3, 6, 6, 6, 9, 9, 9]
[3, 3, 3, 6, 6, 7, 7, 7, 12]
[3, 3, 3, 6, 6, 7, 7, 8, 11]
[3, 3, 3, 6, 6, 7, 7, 9, 10]
[3, 3, 3, 6, 6, 7, 8, 8, 10]
[3, 3, 3, 6, 6, 7, 8, 9, 9]
[3, 3, 3, 6, 6, 8, 8, 8, 9]
[3, 3, 3, 6, 7, 7, 7, 7, 11]
[3, 3, 3, 6, 7, 7, 7, 8, 10]
[3, 3, 3, 6, 7, 7, 7, 9, 9]
[3, 3, 3, 6, 7, 7, 8, 8, 9]
[3, 3, 3, 6, 7, 8, 8, 8, 8]
[3, 3, 3, 7, 7, 7, 7, 7, 10]
[3, 3, 3, 7, 7, 7, 7, 8, 9]
[3, 3, 3, 7, 7, 7, 8, 8, 8]
[3, 3, 4, 5, 6, 6, 6, 6, 15]
[3, 3, 4, 5, 6, 6, 6, 7, 14]
[3, 3, 4, 5, 6, 6, 6, 8, 13]
[3, 3, 4, 5, 6, 6, 6, 9, 12]
[3, 3, 4, 5, 6, 6, 6, 10, 11]
[3, 3, 4, 5, 6, 6, 7, 7, 13]
[3, 3, 4, 5, 6, 6, 7, 8, 12]
[3, 3, 4, 5, 6, 6, 7, 9, 11]
[3, 3, 4, 5, 6, 6, 7, 10, 10]
[3, 3, 4, 5, 6, 6, 8, 8, 11]
[3, 3, 4, 5, 6, 6, 8, 9, 10]
[3, 3, 4, 5, 6, 6, 9, 9, 9]
[3, 3, 4, 5, 6, 7, 7, 7, 12]
[3, 3, 4, 5, 6, 7, 7, 8, 11]
[3, 3, 4, 5, 6, 7, 7, 9, 10]
[3, 3, 4, 5, 6, 7, 8, 8, 10]
[3, 3, 4, 5, 6, 7, 8, 9, 9]
[3, 3, 4, 5, 6, 8, 8, 8, 9]
[3, 3, 4, 5, 7, 7, 7, 7, 11]
[3, 3, 4, 5, 7, 7, 7, 8, 10]
[3, 3, 4, 5, 7, 7, 7, 9, 9]
[3, 3, 4, 5, 7, 7, 8, 8, 9]
[3, 3, 4, 5, 7, 8, 8, 8, 8]
[3, 3, 5, 5, 5, 6, 6, 6, 15]
[3, 3, 5, 5, 5, 6, 6, 7, 14]
[3, 3, 5, 5, 5, 6, 6, 8, 13]
[3, 3, 5, 5, 5, 6, 6, 9, 12]
[3, 3, 5, 5, 5, 6, 6, 10, 11]
[3, 3, 5, 5, 5, 6, 7, 7, 13]
[3, 3, 5, 5, 5, 6, 7, 8, 12]
[3, 3, 5, 5, 5, 6, 7, 9, 11]
[3, 3, 5, 5, 5, 6, 7, 10, 10]
[3, 3, 5, 5, 5, 6, 8, 8, 11]
[3, 3, 5, 5, 5, 6, 8, 9, 10]
[3, 3, 5, 5, 5, 6, 9, 9, 9]
[3, 3, 5, 5, 5, 7, 7, 7, 12]
[3, 3, 5, 5, 5, 7, 7, 8, 11]
[3, 3, 5, 5, 5, 7, 7, 9, 10]
[3, 3, 5, 5, 5, 7, 8, 8, 10]
[3, 3, 5, 5, 5, 7, 8, 9, 9]
[3, 3, 5, 5, 5, 8, 8, 8, 9]
[3, 4, 4, 4, 6, 6, 6, 6, 15]
[3, 4, 4, 4, 6, 6, 6, 7, 14]
[3, 4, 4, 4, 6, 6, 6, 8, 13]
[3, 4, 4, 4, 6, 6, 6, 9, 12]
[3, 4, 4, 4, 6, 6, 6, 10, 11]
[3, 4, 4, 4, 6, 6, 7, 7, 13]
[3, 4, 4, 4, 6, 6, 7, 8, 12]
[3, 4, 4, 4, 6, 6, 7, 9, 11]
[3, 4, 4, 4, 6, 6, 7, 10, 10]
[3, 4, 4, 4, 6, 6, 8, 8, 11]
[3, 4, 4, 4, 6, 6, 8, 9, 10]
[3, 4, 4, 4, 6, 6, 9, 9, 9]
[3, 4, 4, 4, 6, 7, 7, 7, 12]
[3, 4, 4, 4, 6, 7, 7, 8, 11]
[3, 4, 4, 4, 6, 7, 7, 9, 10]
[3, 4, 4, 4, 6, 7, 8, 8, 10]
[3, 4, 4, 4, 6, 7, 8, 9, 9]
[3, 4, 4, 4, 6, 8, 8, 8, 9]
[3, 4, 4, 4, 7, 7, 7, 7, 11]
[3, 4, 4, 4, 7, 7, 7, 8, 10]
[3, 4, 4, 4, 7, 7, 7, 9, 9]
[3, 4, 4, 4, 7, 7, 8, 8, 9]
[3, 4, 4, 4, 7, 8, 8, 8, 8]
[3, 4, 4, 5, 5, 6, 6, 6, 15]
[3, 4, 4, 5, 5, 6, 6, 7, 14]
[3, 4, 4, 5, 5, 6, 6, 8, 13]
[3, 4, 4, 5, 5, 6, 6, 9, 12]
[3, 4, 4, 5, 5, 6, 6, 10, 11]
[3, 4, 4, 5, 5, 6, 7, 7, 13]
[3, 4, 4, 5, 5, 6, 7, 8, 12]
[3, 4, 4, 5, 5, 6, 7, 9, 11]
[3, 4, 4, 5, 5, 6, 7, 10, 10]
[3, 4, 4, 5, 5, 6, 8, 8, 11]
[3, 4, 4, 5, 5, 6, 8, 9, 10]
[3, 4, 4, 5, 5, 6, 9, 9, 9]
[3, 4, 4, 5, 5, 7, 7, 7, 12]
[3, 4, 4, 5, 5, 7, 7, 8, 11]
[3, 4, 4, 5, 5, 7, 7, 9, 10]
[3, 4, 4, 5, 5, 7, 8, 8, 10]
[3, 4, 4, 5, 5, 7, 8, 9, 9]
[3, 4, 4, 5, 5, 8, 8, 8, 9]
[3, 4, 5, 5, 5, 5, 6, 6, 15]
[3, 4, 5, 5, 5, 5, 6, 7, 14]
[3, 4, 5, 5, 5, 5, 6, 8, 13]
[3, 4, 5, 5, 5, 5, 6, 9, 12]
[3, 4, 5, 5, 5, 5, 6, 10, 11]
[3, 4, 5, 5, 5, 5, 7, 7, 13]
[3, 4, 5, 5, 5, 5, 7, 8, 12]
[3, 4, 5, 5, 5, 5, 7, 9, 11]
[3, 4, 5, 5, 5, 5, 7, 10, 10]
[3, 4, 5, 5, 5, 5, 8, 8, 11]
[3, 4, 5, 5, 5, 5, 8, 9, 10]
[3, 4, 5, 5, 5, 5, 9, 9, 9]
[3, 5, 5, 5, 5, 5, 5, 6, 15]
[3, 5, 5, 5, 5, 5, 5, 7, 14]
[3, 5, 5, 5, 5, 5, 5, 8, 13]
[3, 5, 5, 5, 5, 5, 5, 9, 12]
[3, 5, 5, 5, 5, 5, 5, 10, 11]
[4, 4, 4, 4, 5, 6, 6, 6, 15]
[4, 4, 4, 4, 5, 6, 6, 7, 14]
[4, 4, 4, 4, 5, 6, 6, 8, 13]
[4, 4, 4, 4, 5, 6, 6, 9, 12]
[4, 4, 4, 4, 5, 6, 6, 10, 11]
[4, 4, 4, 4, 5, 6, 7, 7, 13]
[4, 4, 4, 4, 5, 6, 7, 8, 12]
[4, 4, 4, 4, 5, 6, 7, 9, 11]
[4, 4, 4, 4, 5, 6, 7, 10, 10]
[4, 4, 4, 4, 5, 6, 8, 8, 11]
[4, 4, 4, 4, 5, 6, 8, 9, 10]
[4, 4, 4, 4, 5, 6, 9, 9, 9]
[4, 4, 4, 4, 5, 7, 7, 7, 12]
[4, 4, 4, 4, 5, 7, 7, 8, 11]
[4, 4, 4, 4, 5, 7, 7, 9, 10]
[4, 4, 4, 4, 5, 7, 8, 8, 10]
[4, 4, 4, 4, 5, 7, 8, 9, 9]
[4, 4, 4, 4, 5, 8, 8, 8, 9]
[4, 4, 4, 5, 5, 5, 6, 6, 15]
[4, 4, 4, 5, 5, 5, 6, 7, 14]
[4, 4, 4, 5, 5, 5, 6, 8, 13]
[4, 4, 4, 5, 5, 5, 6, 9, 12]
[4, 4, 4, 5, 5, 5, 6, 10, 11]
[4, 4, 4, 5, 5, 5, 7, 7, 13]
[4, 4, 4, 5, 5, 5, 7, 8, 12]
[4, 4, 4, 5, 5, 5, 7, 9, 11]
[4, 4, 4, 5, 5, 5, 7, 10, 10]
[4, 4, 4, 5, 5, 5, 8, 8, 11]
[4, 4, 4, 5, 5, 5, 8, 9, 10]
[4, 4, 4, 5, 5, 5, 9, 9, 9]
[4, 4, 5, 5, 5, 5, 5, 6, 15]
[4, 4, 5, 5, 5, 5, 5, 7, 14]
[4, 4, 5, 5, 5, 5, 5, 8, 13]
[4, 4, 5, 5, 5, 5, 5, 9, 12]
[4, 4, 5, 5, 5, 5, 5, 10, 11]
[4, 5, 5, 5, 5, 5, 5, 5, 15]
In the integers, you get an additional 111 solutions:
[-3, 6, 6, 6, 6, 6, 6, 6, 15]
[-3, 6, 6, 6, 6, 6, 6, 7, 14]
[-3, 6, 6, 6, 6, 6, 6, 8, 13]
[-3, 6, 6, 6, 6, 6, 6, 9, 12]
[-3, 6, 6, 6, 6, 6, 6, 10, 11]
[-3, 6, 6, 6, 6, 6, 7, 7, 13]
[-3, 6, 6, 6, 6, 6, 7, 8, 12]
[-3, 6, 6, 6, 6, 6, 7, 9, 11]
[-3, 6, 6, 6, 6, 6, 7, 10, 10]
[-3, 6, 6, 6, 6, 6, 8, 8, 11]
[-3, 6, 6, 6, 6, 6, 8, 9, 10]
[-3, 6, 6, 6, 6, 6, 9, 9, 9]
[-3, 6, 6, 6, 6, 7, 7, 7, 12]
[-3, 6, 6, 6, 6, 7, 7, 8, 11]
[-3, 6, 6, 6, 6, 7, 7, 9, 10]
[-3, 6, 6, 6, 6, 7, 8, 8, 10]
[-3, 6, 6, 6, 6, 7, 8, 9, 9]
[-3, 6, 6, 6, 6, 8, 8, 8, 9]
[-3, 6, 6, 6, 7, 7, 7, 7, 11]
[-3, 6, 6, 6, 7, 7, 7, 8, 10]
[-3, 6, 6, 6, 7, 7, 7, 9, 9]
[-3, 6, 6, 6, 7, 7, 8, 8, 9]
[-3, 6, 6, 6, 7, 8, 8, 8, 8]
[-3, 6, 6, 7, 7, 7, 7, 7, 10]
[-3, 6, 6, 7, 7, 7, 7, 8, 9]
[-3, 6, 6, 7, 7, 7, 8, 8, 8]
[-3, 6, 7, 7, 7, 7, 7, 7, 9]
[-3, 6, 7, 7, 7, 7, 7, 8, 8]
[-3, 7, 7, 7, 7, 7, 7, 7, 8]
[-2, 5, 6, 6, 6, 6, 6, 6, 15]
[-2, 5, 6, 6, 6, 6, 6, 7, 14]
[-2, 5, 6, 6, 6, 6, 6, 8, 13]
[-2, 5, 6, 6, 6, 6, 6, 9, 12]
[-2, 5, 6, 6, 6, 6, 6, 10, 11]
[-2, 5, 6, 6, 6, 6, 7, 7, 13]
[-2, 5, 6, 6, 6, 6, 7, 8, 12]
[-2, 5, 6, 6, 6, 6, 7, 9, 11]
[-2, 5, 6, 6, 6, 6, 7, 10, 10]
[-2, 5, 6, 6, 6, 6, 8, 8, 11]
[-2, 5, 6, 6, 6, 6, 8, 9, 10]
[-2, 5, 6, 6, 6, 6, 9, 9, 9]
[-2, 5, 6, 6, 6, 7, 7, 7, 12]
[-2, 5, 6, 6, 6, 7, 7, 8, 11]
[-2, 5, 6, 6, 6, 7, 7, 9, 10]
[-2, 5, 6, 6, 6, 7, 8, 8, 10]
[-2, 5, 6, 6, 6, 7, 8, 9, 9]
[-2, 5, 6, 6, 6, 8, 8, 8, 9]
[-2, 5, 6, 6, 7, 7, 7, 7, 11]
[-2, 5, 6, 6, 7, 7, 7, 8, 10]
[-2, 5, 6, 6, 7, 7, 7, 9, 9]
[-2, 5, 6, 6, 7, 7, 8, 8, 9]
[-2, 5, 6, 6, 7, 8, 8, 8, 8]
[-2, 5, 6, 7, 7, 7, 7, 7, 10]
[-2, 5, 6, 7, 7, 7, 7, 8, 9]
[-2, 5, 6, 7, 7, 7, 8, 8, 8]
[-2, 5, 7, 7, 7, 7, 7, 7, 9]
[-2, 5, 7, 7, 7, 7, 7, 8, 8]
[-1, 4, 6, 6, 6, 6, 6, 6, 15]
[-1, 4, 6, 6, 6, 6, 6, 7, 14]
[-1, 4, 6, 6, 6, 6, 6, 8, 13]
[-1, 4, 6, 6, 6, 6, 6, 9, 12]
[-1, 4, 6, 6, 6, 6, 6, 10, 11]
[-1, 4, 6, 6, 6, 6, 7, 7, 13]
[-1, 4, 6, 6, 6, 6, 7, 8, 12]
[-1, 4, 6, 6, 6, 6, 7, 9, 11]
[-1, 4, 6, 6, 6, 6, 7, 10, 10]
[-1, 4, 6, 6, 6, 6, 8, 8, 11]
[-1, 4, 6, 6, 6, 6, 8, 9, 10]
[-1, 4, 6, 6, 6, 6, 9, 9, 9]
[-1, 4, 6, 6, 6, 7, 7, 7, 12]
[-1, 4, 6, 6, 6, 7, 7, 8, 11]
[-1, 4, 6, 6, 6, 7, 7, 9, 10]
[-1, 4, 6, 6, 6, 7, 8, 8, 10]
[-1, 4, 6, 6, 6, 7, 8, 9, 9]
[-1, 4, 6, 6, 6, 8, 8, 8, 9]
[-1, 4, 6, 6, 7, 7, 7, 7, 11]
[-1, 4, 6, 6, 7, 7, 7, 8, 10]
[-1, 4, 6, 6, 7, 7, 7, 9, 9]
[-1, 4, 6, 6, 7, 7, 8, 8, 9]
[-1, 4, 6, 6, 7, 8, 8, 8, 8]
[-1, 4, 6, 7, 7, 7, 7, 7, 10]
[-1, 4, 6, 7, 7, 7, 7, 8, 9]
[-1, 4, 6, 7, 7, 7, 8, 8, 8]
[-1, 4, 7, 7, 7, 7, 7, 7, 9]
[-1, 4, 7, 7, 7, 7, 7, 8, 8]
[-1, 5, 5, 6, 6, 6, 6, 6, 15]
[-1, 5, 5, 6, 6, 6, 6, 7, 14]
[-1, 5, 5, 6, 6, 6, 6, 8, 13]
[-1, 5, 5, 6, 6, 6, 6, 9, 12]
[-1, 5, 5, 6, 6, 6, 6, 10, 11]
[-1, 5, 5, 6, 6, 6, 7, 7, 13]
[-1, 5, 5, 6, 6, 6, 7, 8, 12]
[-1, 5, 5, 6, 6, 6, 7, 9, 11]
[-1, 5, 5, 6, 6, 6, 7, 10, 10]
[-1, 5, 5, 6, 6, 6, 8, 8, 11]
[-1, 5, 5, 6, 6, 6, 8, 9, 10]
[-1, 5, 5, 6, 6, 6, 9, 9, 9]
[-1, 5, 5, 6, 6, 7, 7, 7, 12]
[-1, 5, 5, 6, 6, 7, 7, 8, 11]
[-1, 5, 5, 6, 6, 7, 7, 9, 10]
[-1, 5, 5, 6, 6, 7, 8, 8, 10]
[-1, 5, 5, 6, 6, 7, 8, 9, 9]
[-1, 5, 5, 6, 6, 8, 8, 8, 9]
[-1, 5, 5, 6, 7, 7, 7, 7, 11]
[-1, 5, 5, 6, 7, 7, 7, 8, 10]
[-1, 5, 5, 6, 7, 7, 7, 9, 9]
[-1, 5, 5, 6, 7, 7, 8, 8, 9]
[-1, 5, 5, 6, 7, 8, 8, 8, 8]
[-1, 5, 5, 7, 7, 7, 7, 7, 10]
[-1, 5, 5, 7, 7, 7, 7, 8, 9]
[-1, 5, 5, 7, 7, 7, 8, 8, 8]
In the rationals, you can construct infinitely many solutions by taking any of solutions above, taking two elements a and b smaller than 6 in that data set, letting x equal max{a,b} and adding some rational number r < 6-x to one of them and subtracting it from the other. This way, the total sum won't change and since one of the elements gets closer to 6 (the mean) by r and one gets away further from 6 by r, the MAD doesn't change either.
For example, take [3, 3, 3, 6, 6, 6, 9, 9, 9]:
Now let’s add 0.5 to one of the 3’s and subtract 0.5 from one of the 3’s and you get:
[2.5, 3, 3.5, 6, 6, 6, 9, 9, 9]
Instead of 0.5, I could take any real number between 0 and 3, which there are infinitely many of.