Absolute Deviation

Directions: Using only numbers 1-9 (without repeating any number), fill in the boxes 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

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Greatest Common Factor

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5 comments

  1. 9,8,7,65,43,21

  2. Is this asking about mean absolute deviation or just absolute deviation?

    • Rudolf Österreicher

      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.

  3. Rudolf Österreicher

    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]

    • Rudolf Österreicher

      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]

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