Female+Cicada+MAD

=Mean Absolute Deviation of Female Cicada Wing Length Data= Date developed: 9/3/12 Date posted: 12/31/12 Return to Mean Absolute Deviation

TinkerPlots File

One of the difficulties I have encountered when teaching the concept of mean absolute deviation is nasty numbers. If the mean of a given data set is not a "nice" decimal, my students quickly get lost in number crunching. Also, answers don't match due to rounding error. In order to keep the focus on the concept, and not the calculation I often make adjustments to the data that I am using. Also, I trim data sets to 8-12 values when "by-hand" calculations are required. In the Female Cicada data set, the mean wing length is 29.5 mm. Personally, I like this because it is different from any of the given data values. But, if you are introducing this topic to your students, you might want to adjust one or more of the lengths so the mean is an integer. In what follows below, I will manipulate the Female Cicada data so that the mean of the WingL variable is an integer. I have added five columns into the case table so I can see all of the values for every calculation needed to find the MAD.
 * Goal**

1. Note that there are 8 cicadas, so the sum needs to be be a multiple of 8.
 * Manipulate the data**

2. Since 236/8 is 29.5, you can adjust this to 232 by changing one or more of the values. I chose to adjust down due to the fact that four of the 8 cicadas has a wing length of 30 millimeters (and I did not want a mean of 30 mm).

3. I sorted the columns so that I can see the range of values. This helps me see that I really don't want another 30.

In order to preserve the initial data set, I created a copy (actually two copies).
 * Adjusted Data Sets**

In my first attempt, I changed two of the 30s to 28 and that took the sum down to 232. But, now the MAD is one. Since there are seven ones in the abs_dif column, it might be difficult to find a student error.

In my second attempt to change the data, the mean is still 29, but the MAD is 1.25 I think that this works better because the MAD will typically not be an integer. Also, I can quickly find an error in a student's calculation of the MAD.

I often duplicate and then manipulate data sets when I want to create additional problem sets or assessment items. The trick is to keep track of them!

The first three plots below illustrate the steps used to calculate the MAD. The first dot plot shows the female wing length data. The second plot shows the distance from the mean for each cicada's wing length. I like to ask students why the mean is zero! The third plot shows a dot plot of the absolute value of the differences. The mean tool is used to locate the MAD of 1.125 mm. You might ask your students to estimate the value of the mean before using the mean tool.
 * Graphically Calculate the MAD**

The forth plot shows the results of using the ruler tool to calculate the MAD.

TinkerPlots File

Please let me know if you have any questions or comments with this activity.