# Lesson 11

### Lesson Narrative

In a previous lesson, students computed and interpreted distances of data points from the mean. In this lesson, they take that experience to make sense of the formal idea of 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.

### Learning Goals

Teacher Facing

• 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, i.e., a single number summarizing how spread out the data set is.

### Student Facing

Let's study distances between data points and the mean and see what they tell us.

### Required Preparation

If students are playing the optional Game of 22, prepare one standard deck of 52 playing cards for every 2–3 students.

### Student Facing

• I can find the MAD for a set of data.
• I know what the mean absolute deviation (MAD) measures and what information it provides.

### Glossary Entries

• average

The average is another name for the mean of a data set.

For the data set 3, 5, 6, 8, 11, 12, the average is 7.5.

$$3+5+6+8+11+12=45$$

$$45 \div 6 = 7.5$$

• mean

The mean is one way to measure the center of a data set. We can think of it as a balance point. For example, for the data set 7, 9, 12, 13, 14, the mean is 11.

To find the mean, add up all the numbers in the data set. Then, divide by how many numbers there are. $$7+9+12+13+14=55$$ and $$55 \div 5 = 11$$.

The mean absolute deviation is one way to measure how spread out a data set is. Sometimes we call this the MAD. For example, for the data set 7, 9, 12, 13, 14, the MAD is 2.4. This tells us that these travel times are typically 2.4 minutes away from the mean, which is 11.

To find the MAD, add up the distance between each data point and the mean. Then, divide by how many numbers there are.

$$4+2+1+2+3=12$$ and $$12 \div 5 = 2.4$$

• measure of center

A measure of center is a value that seems typical for a data distribution.

Mean and median are both measures of center.

### Print Formatted Materials

For access, consult one of our IM Certified Partners.