# Lesson 5

Calculating Measures of Center and Variability

### Lesson Narrative

This lesson is optional because it revisits below grade-level content. If the pre-unit diagnostic assessment indicates that your students know how to calculate the mean, median, mean absolute deviation (MAD), and interquartile range (IQR) then this lesson may be safely skipped. This lesson connects to upcoming work because students will interpret data using measures of center and measures of variability throughout the unit, so it is important that they understand what these statistics mean. When students explain the MAD using the meter stick example they are engaging in MP2 because they were reasoning abstractly and quantitatively by interpreting the MAD in context.

### Learning Goals

Teacher Facing

• Calculate mean absolute deviation, interquartile range, mean, and median.

### Student Facing

• Let’s calculate measures of center and measures of variability and know which are most appropriate for the data.

### Required Preparation

You will need a meter stick and 14 pennies (or other small weights) for a demonstration. An optional blackline master is included as a graphic organizer for computing interquartile range. One copy of the blackline master contains 2 graphic organizers.

### Student Facing

• I can calculate mean absolute deviation, interquartile range, mean, and median for a set of data.

Building On

Building Towards

### Glossary Entries

• bell-shaped distribution

A distribution whose dot plot or histogram takes the form of a bell with most of the data clustered near the center and fewer points farther from the center.

• bimodal distribution

A distribution with two very common data values seen in a dot plot or histogram as distinct peaks. In the dot plot shown, the two common data values are 2 and 7,

• skewed distribution

A distribution where one side of the distribution has more values farther from the bulk of the data than the other side, so that the mean is not equal to the median. In the dot plot shown, the data values on the left, such as 1, 2, and 3, are further from the bulk of the data than the data values on the right.