# Lesson 19

Comparing Populations With Friends

### Lesson Narrative

Students continue to practice comparing populations by using samples from each population. Outside of the classroom, people who wish to compare groups will not usually have all of the useful statistics presented to them in a nice package, so they will need to determine what information to gather and then work through the comparison process. In this lesson, students are paired so that one student is presented with a situation and question while the other student has information to help solve the question. They must work together to answer the question by asking their own questions and explaining how each piece of information will be useful. An optional activity is also included in which students are asked to compare data from a sample of one population to statistics from a sample of a second population.

### Learning Goals

Teacher Facing

• Apply reasoning about center and spread to determine whether two populations are likely to be meaningfully different, and explain (orally and in writing) the reasoning.
• Coordinate (orally) visual displays of data with descriptions of shape, measures of center, and measures of spread.
• Determine what information is needed to solve problems about using samples to compare populations. Ask questions to elicit that information.

### Student Facing

Let's ask important questions to compare groups.

### Required Preparation

One copy of the blackline master from Comparing Populations cut into cards for every 2 students.

### Student Facing

• I can decide what information I need to know to be able to compare two populations based on a sample from each.

Building On

### 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.

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