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.

### Hint

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?

### Answer

Source: Robert Kaplinsky with help from Pamela Franklin

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?

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.

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?

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

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.

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.

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

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.

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.

How are those identical box plots? the first data set has a lower quartile of 3 while the second data set has a lower quartile of 4.