# Lesson 15

Estimating Population Measures of Center

### Lesson Narrative

In this lesson students calculate measures of center and variation for samples from different populations and consider the meaning of these quantities in terms of the situation (MP2). Students see that when there is less variability in the data from different samples from a population, then there is reason to believe that the measure of center from a sample is a better estimate for the measure of center from a population than when a sample has greater variability (MP7).

### Learning Goals

Teacher Facing

• Calculate and interpret (orally and in writing) the mean absolute deviation of a sample.
• Generalize that an estimate for the center of a population distribution is more likely to be accurate when it is based on a random sample with less variability.
• Use the mean of a random sample to make inferences about the population, and explain (orally and in writing) the reasoning.

### Student Facing

Let’s use samples to estimate measures of center for the population.

### Student Facing

• I can consider the variability of a sample to get an idea for how accurate my estimate is.
• I can estimate the mean or median of a population based on a sample of the 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