Unit 8, Lesson 11
Variability and MAD
Grade 6
Preparation
Lesson Narrative
In this lesson, students make sense of the mean absolute deviation (MAD). Students learn that the MAD is the average distance of data points from the mean. They use their knowledge of how to calculate and interpret the mean to calculate (MP8) and interpret (MP2) the MAD.
Students also learn that we think of the MAD as a measure of variability or a measure of spread of a distribution. They compare distributions with the same mean but different MADs, and recognize that the centers are the same but the distribution with the larger MAD has greater variability, or spread.
- Calculate the mean absolute deviation (MAD) for a data set and interpret what it tells us about the situation.
- Compare and contrast (in writing) distributions that have the same mean, but different amounts of variability.
- Comprehend that “mean absolute deviation (MAD)” is a measure of variability, that is, a single number summarizing how spread out the data set is.
Let's study distances between data points and the mean and see what they tell us.
Required Materials
Activity 4
Required Preparation
If students are playing the optional Game of 22, prepare one standard deck of 52 playing cards for every 2–3 students.
The mean absolute deviation (MAD) is one way to measure how spread out a data set is. To find the MAD, find the distance between each data value and the mean. Add all the distances. Then divide by how many distances there are.
- Data set: 7, 9, 12, 13, 14
- Add distances:
- Divide by number of distances:
The MAD is 2.4. So, these travel times are typically 2.4 minutes away from the mean of 11 minutes.