Addressing Standard 7.SP.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Addressing Standard 7.SP.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Addressing Standard 7.SP.4

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Objectives

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.

Online Workbook

Take me to the website.

Lesson Summary

Some populations have greater variability than others. For example, we would expect greater variability in the weights of dogs at a dog park than at a beagle meetup.

Dog park:

A picture of 2 small dogs, 2 medium sized dogs, and 3 large dogs.

Mean weight: 12.8 kg

MAD: 2.3 kg

Beagle meetup:

A picture of 7 similar sized beagle dogs.

Mean weight: 10.1 kg

MAD: 0.8 kg

The lower MAD indicates there is less variability in the weights of the beagles. We would expect that the mean weight from a sample that is randomly selected from a group of beagles will provide a more accurate estimate of the mean weight of all the beagles than a sample of the same size from the dogs at the dog park.

In general, a sample of a similar size from a population with less variability is more likely to have a mean that is close to the population mean.