# Lesson 10

Finding and Interpreting the Mean as the Balance Point

### Lesson Narrative

In the previous lesson, students interpreted the mean as a fair-share value—i.e., what each group member would have if all the values are distributed such that all members have the same amount. In this lesson, students use the structure of the data (MP7) to interpret the mean as the balance point of a numerical distribution. They calculate how far away each data point is from the mean and study how the distances on either side of the mean compare.

Students connect this interpretation to why we call the mean a measure of the center of a distribution and, through this interpretation, begin to see how the mean is useful in characterizing a “typical” value for the group. Students continue to practice calculating the mean of a data set (MP8) and interpreting it in context (MP2).

### Learning Goals

Teacher Facing

• Calculate and interpret (orally and in writing) distances between data points and the mean of the data set.
• Interpret diagrams that represent the mean as a “balance point” for both symmetrical and non-symmetrical distributions.
• Represent the mean of a data set on a dot plot and interpret it in the context of the situation.

### Student Facing

Let's look at another way to understand the mean of a data set.

### Student Facing

• I can describe what the mean tells us in the context of the data.
• I can explain how the mean represents a balance point for the data on a dot plot.

### 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 $$55 \div 5 = 11$$.

• 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.