# Lesson 12

Using Mean and MAD to Make Comparisons

### Lesson Narrative

In this lesson, students continue to develop their understanding of the mean and MAD as measures of center and spread as well as interpret these values in context. They practice computing the mean and the MAD for distributions; compare distributions with the same MAD but different means; and interpret the mean and MAD in the context of the data (MP2).

### Learning Goals

Teacher Facing

• Compare (orally and in writing) the means and mean absolute deviations of different distributions, specifically those with the same MAD but different means.
• Interpret the mean and mean absolute deviation (MAD) in the context of the data.

### Student Facing

Let's use mean and MAD to describe and compare distributions.

### Student Facing

• I can say what the MAD tells us in a given context.
• I can use means and MADs to compare groups.

Building Towards

### 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.

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