# 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