# Lesson 18

Comparing Populations Using Samples

### Lesson Narrative

In previous lessons, students examined the distributions of two entire populations to decide whether or not they were very different. In this lesson, students use samples to make comparative inferences about populations.

Students see that if samples of two different populations have only a small difference between their measures of center (relative to their variability), then we cannot say that there is a meaningful difference between the measures of center of the populations (MP2). Due to sampling variability, it is possible that the two populations may not be very different. However, if samples from two different populations have a large difference between their measures of center (relative to their variability), then we can say that there is likely to be a meaningful difference between the measures of center of the two populations.

### Learning Goals

Teacher Facing

• Calculate the difference between the mean or median of two samples from different populations, and express it as a multiple of the MAD or IQR.
• Interpret a pair of box plots, including the amount of visual overlap between the two distributions.
• Justify (orally and in writing) whether there is likely to be a meaningful difference between two populations, based on a sample from each population.

### Student Facing

Let’s compare different populations using samples.

### Student Facing

• I can calculate the difference between two medians as a multiple of the interquartile range.
• I can determine whether there is a meaningful difference between two populations based on a sample from each population.

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.

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