Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create a set of data with the largest possible absolute deviation.
Hint
What are the properties of a population with a higher absolute deviation? A lower absolute deviation?
Answer
1, 2, 3, 74, 85, 96
Source: Mark Alvaro
9,8,7,65,43,21
Is this asking about mean absolute deviation or just absolute deviation?
The total absolute deviation (TAD) is proportional to the mean absolute deviation (MAD), so if you found the greatest possible TAD, you automatically get the greatest possible MAD by dividing by the number of elements in the data set.
The greatest possible MAD is 41.5 (or TAD = 249) and there are 6 data sets with a MAD of 41.5:
[1, 2, 3, 74, 85, 96]
[1, 2, 3, 74, 86, 95]
[1, 2, 3, 75, 84, 96]
[1, 2, 3, 75, 86, 94]
[1, 2, 3, 76, 84, 95]
[1, 2, 3, 76, 85, 94]
The smallest possible MAD btw is 26/3 and there are 2 data sets with a MAD of 26/3:
[7, 8, 9, 16, 24, 35]
[7, 8, 9, 16, 25, 34]
1,000,000