# Statistics and Probability / Sample Means

Grade Level 7,8
Activity 20 of 24
In this lesson, students use simulation to explore how sample means (and medians) vary from sample to sample when repeated samples are taken from the same population.

## Planning and Resources

Objectives
Students distinguish sampling variability among sample statistics from the variability within a sample. They recognize that sampling distributions of sample means are mound shaped and that as the sample size increases, the spread decreases.

Vocabulary
sample
sample size
mean
sampling distribution
simulated sampling distribution

Standard:

## Lesson Snapshot

#### Understanding

The mean and MAD of a large random sample drawn from a population can give some indication of the population mean.

### What to look for

In order to have a predictable shape and spread for a simulated sampling distribution, the sample size must be large.

### Sample Assessment

Identify each statement as true or false.

a) The larger the sample size the more likely that a sample mean will be farther from the population mean.
Answer: False

b) The larger the sample size the more likely a sample mean will approximate the population mean.
Answer: True

c) All simulated distributions of sample means, no matter what sample size, will be mound shaped and symmetric.
Answer: False

#### The Big Idea

The mean of a simulated sampling distribution of sample means for a given sample size is close to the mean of the population from which the samples were drawn.

### What are the students doing?

Students investigate the relationship between sample size and the center, shape, and spread of the sampling distribution of sample means.

### What is the teacher doing?

Be sure students recognize that regardless of the shape of the population distribution, the simulated sampling distribution of means for a large sample size will be fairly mound shaped and symmetric about the mean of the population.