Understanding Mean Absolute Deviation (MAD)

Have you ever looked at a group of numbers and wondered how spread out they are? The mean might tell you the average, but it doesn’t show how close or far each value is from that average. Mean Absolute Deviation (MAD) helps you measure the variation in a data set. This playsheet guides you step-by-step so you can see not only what the numbers say, but how they behave. You learn that MAD is like a detective tool—it uncovers the hidden movement within a set of data.

As you complete each activity, you’ll begin by calculating the mean of a data set. Once you find the average, you’ll subtract the mean from each data value to discover how far each number is from it. These differences show you the distance between individual numbers and the center of the data. You start noticing that numbers with big differences increase the “spread,” while smaller differences show consistency.

Next, you’ll explore why we use absolute values when calculating MAD. You’ll learn that absolute value turns every difference into a positive number, removing negative signs that could cancel out the truth of your data. You’ll discover how absolute value keeps the math fair and ensures every variation counts. This step helps you understand why MAD uses distance—not direction—to describe how data changes.