# Lesson 4

Describing Distributions

### Lesson Narrative

This lesson is optional since it reviews concepts learned in prior grades. If students understand how to describe distribution shapes as well as the meaning of mean, median, and standard deviation, this lesson may be safely skipped.

The mathematical purpose of this lesson is to interpret the standard deviation as a measure of variability and to describe the shapes and properties of distributions. The work of this lesson connects to previous work because students investigated the importance of randomness in selecting a sample and the importance of randomness in assigning participants to groups for an experimental study. The properties of bell-shaped distributions are a particular focus. Although it is rare to have perfectly bell-shaped distributions in reality, approximately bell-shaped distributions can be modeled by a normal curve, which will be the focus of the next several lessons. When students articulate things they notice about a dot plot, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). When students trade roles explaining their thinking and listening about the shape of a distribution and summary statistics for a dot plot, they are explaining their reasoning and critiquing the reasoning of others (MP3).

### Learning Goals

Teacher Facing

• Describe (orally and in writing) various distributions as skewed, symmetric, or bell-shaped.
• Recall how to interpret (orally and in writing) the standard deviation as a measure of variability.

### Student Facing

• Let’s remember what standard deviation means, and discuss distributions.

### Student Facing

• I can describe a distribution using the characteristics of its shape, center, and spread.
• I can use the standard deviation to describe the variability in a distribution.