# 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.

### 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?

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

## Solving One-Step Inequalities with Addition

Directions: Using the digits 0 to 9 at most one time each, place a digit …

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.

• 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?

2. 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.

3. 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.

4. 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

5. 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.

6. Person aka kaleya

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.

7. 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.