Mean Absolute Deviation (MAD)

The concept and method to find the mean absolute deviation is identical to finding the median absolution page. I completed the median absolute value (in great detail) because it is much easier to work with an integer value.

Female Cicada Wing Length
This activity file consists of specific information for educators wanting to teach the concept of Mean Absolute Deviation. The primary goal is to adjust a data set so that the computation involved in finding the MAD is secondary to teaching the concept. Teachers should have a basic level of knowledge of case tables and plots. The case table is used to complete the mathematics involved in computing the MAD. Plots are used to illustrate the calculations (finding the mean of the absolute values of the differences from the mean). The horizontal ruler tool is used to quickly calculate the Mean Absolute Deviation.

Male Cicada Wing Length
This activity file consists of the TinkerPlots file with comments directed to the teacher. This activity is an extension to the Female Cicada activity listed above. The MAD is approximately twice that of the Female Cicada data set. MAD is used to discuss similarities or differences in variability between data sets.

Test Score MAD
The MAD for student test scores for two different math classes are calculated and compared in one TinkerPlots graph. The completed example and file are found on this page.

Sunflower Height MAD
This series of files provide additional data sets. I used these here to introduce the -1.00 to 1.00 Average Deviation Hat Plot. While our middle school students may not need to know this particular concept, it is important that educators see the relationship between MAD and the standard deviation. Click here for a lesson on standard deviation.

Study Time MAD
This activity examines three different sets of study time data for 28 students in separate classes. The data in each class is symmetric with one difference. Class one has a uniform distribution, class two is mound shaped and class three is U shaped. The goal is to explore the variability of the three distributions noting the effect of the shape.
Source: Developing Essential Understanding of Statistics: Grades 6-8, NCTM, 2013

Stopping Distances
Find the Mean Absolute Deviation for the small and large sedans. Discuss the variability.

MAD on Desmos
Thirteen movable points are show within a domain of [0,20]. The mean and the MAD's range is shown.

MAD quiz questions