# Lesson 17

### Lesson Narrative

This lesson is optional. It goes beyond necessary grade-level standards to examine the accuracy of estimates for population characteristics based on many samples. The lesson builds a solid foundation for future grades to build upon, but may be shortened or skipped due to time constraints.

In this lesson, students continue to look at multiple samples from the same population. Examining the structure of dot plots composed of the means from several samples, they see that different samples from the same population can have different means, but that most of these means cluster around the mean of the population (MP7). They consider how far off their estimate might be if they didn’t know the mean of the population but they did know the sample mean. Additionally, students see that larger samples usually produce sample means that are less variable from one another and can more accurately estimate population means.

### Learning Goals

Teacher Facing

• Compare and contrast (orally) a distribution of sample means and the distribution of the population.
• Generalize that an estimate for the center of a population distribution is more likely to be accurate when it is based on a larger random sample.
• Interpret (orally and in writing) a dot plot that displays the means of multiple samples from the same population.

### Student Facing

Let’s compare samples from the same population.

### Required Preparation

For the "Reaction Population" activity, prepare a large number line for the class to use as a dot plot of their sample means from the warm-up of this lesson. Provide students with sticky notes to include as dots for this dot plot.

### Student Facing

• I can use the means from many samples to judge how accurate an estimate for the population mean is.
• I know that as the sample size gets bigger, the sample mean is more likely to be close to the population mean.

Building On

Building Towards

### Glossary Entries

• interquartile range (IQR)

The interquartile range is one way to measure how spread out a data set is. We sometimes call this the IQR. To find the interquartile range we subtract the first quartile from the third quartile.

For example, the IQR of this data set is 20 because $$50-30=20$$.

 22 29 30 31 32 43 44 45 50 50 59 Q1 Q2 Q3
• proportion

A proportion of a data set is the fraction of the data in a given category.

For example, a class has 18 students. There are 2 left-handed students and 16 right-handed students in the class. The proportion of students who are left-handed is $$\frac{2}{20}$$, or 0.1.