# Lesson 9

Variability in Samples

### Lesson Narrative

The purpose of this lesson is for students to understand that random samples produce different estimates for population characteristics and to gain a conceptual understanding of using the margin of error to estimate a population characteristic from a sample statistic. The work of this lesson connects to previous work because students compared estimates using a model to data collected from simulations. The work of this lesson connects to upcoming work because students will take random samples and report an estimate for the population mean with an associated margin of error. Students encounter the term margin of error which is defined as the maximum expected difference between an estimate for a population characteristic and the actual value of the population characteristic. When students make connections between standard deviation and margin of error to estimate a plausible interval for a population mean they are looking for and making use of structure (MP7).

### Learning Goals

Teacher Facing

• Comprehend that random samples produce different estimates for population characteristics.
• Describe (orally and in writing) the importance of margin of error when reporting an estimate for a population characteristic based on a sample statistic.

### Student Facing

• Let’s explore how samples can be different.

### Required Preparation

For the warm-up activity Selecting Samples students each need a copy of the blackline master and either a number cube or a device that can run the applet in the digital version.

Two data sets will be collected from the students from which histograms will be made and used in the following activity. Acquire devices that can run GeoGebra (recommended) or other statistical technology. It is ideal if each student has their own device. (A GeoGebra Statistics tool is available under Math Tools.)

### Student Facing

• I can estimate the margin of error using the mean and standard deviation.
• I understand that sample means and proportions can be representative of the overall population.
• I understand that sample means and proportions vary.

Building Towards

### Glossary Entries

• margin of error

The maximum expected difference between an estimate for a population characteristic and the actual value of the population characteristic.

### Print Formatted Materials

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