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Mean Absolute Deviation

Directions: Give an example of two sets of numbers that form identical box plots (also called box-and-whisker plots) but have different mean absolute deviation values.



What values of two sets of numbers have to be the same to form the same box plot?  What values are left that could be changed?



I believe that there should be an infinite quantity of answers.  One example is {2, 4, 6, 8, 20} and {2, 4, 4, 4, 6, 6, 6, 8, 8, 8, 20}.  They both produce identical box plots but the first set has a mean absolute deviation of 4.8 while the second set has a mean absolute deviation of ~2.98.

Source: Robert Kaplinsky with help from Pamela Franklin

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  1. Wouldn’t the mean absolute deviation of the second data set be approximately 2.98? The mean would be 6.91. Also the mean absolute deviation can never be negative, correct? Or am I missing something?

    • Robert Kaplinsky

      Thanks for catching this Pamela. Here’s what I’m seeing:
      – I somehow calculated MAD incorrectly. The first set has a MAD of 4.8 and the second of, like you said, ~2.98.
      – In regards to MAD never being negative, you are correct. Perhaps the ~6.91 looked like a -6.91? The first one had a tilda for approximately and the second one had a negative.

      Either way, I’ll fix this accordingly.

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