Overview

When you taste sour milk you know right away that the rest of the milk is sour — you have used a sample to make a decision. This lesson helps students understand when it would be necessary to use a sample.

Objective

Students will understand how to analyze if a sample was gathered appropriately and what situations justify the use of samples.

Standards Addressed

Mathematics — Data Analysis

Grade 7

Statistical Methods, Benchmark D

05. Compare data from two or more samples to determine how sample selection can influence results.

 

Grade 8

Statistical Methods, Benchmark D

08. Describe how the relative size of a sample compared to the target population affects the validity of predictions.

 

Procedure

1. Introduce the vocabulary words population, sample and census, which are listed in the Choosing a Sample handout. Ask the class the following: Is population always people? Answer: No, population is any group where 100% of it is used. It could be all the fish in a lake or all the students in a school. Is there only one census? When is this census done? Answer: There is only one US Census every 10 years, however a census is anytime you use the whole population.

2. Divide students into pairs.

3. Ask the students to read the advertisement from Benecol, discuss the statements made and complete the handout ith their partners.

4. Discuss the responses as the class.

Possible Answers

Situation	Sample	Census	Why
Length of battery life	x		Could not test every battery
Accurate count of the number of people in the world		x	Would be very difficult to achieve, but would be a census
Your blood	x		Would merely want a sample of your blood to be tested rather than all of your blood
Reasons for absence from school	x	x	Could be either, depending on how data is to be used
Safety crash tests on cars	x		Wouldn’t want to crash all of the cars
Best pie contest	x		Don’t want to eat the whole pie

 

You want to tell people about your city so you decide to sample the population. Tell if they are good or bad samples and why.

Sample	Good or Bad and Why
Teenagers	Bad — not representative of your entire city
People whose name begin with P	Good — it is assumed that names beginning with P would cover all ages and genders, but would be difficult to accomplish
People at the local airport	Bad — there would be a lot of travelers at the airport so your city might not be represented
People in restaurants	Bad — would be random, but would omit people who could not afford to eat at restaurants
Every 10th person in the telephone book	Bad — omits people who don’t have phones or have unlisted numbers

Evaluation

The goal of this lesson is discussion. Answers will vary on the student handout.

If you choose to grade it, two points could be given for each of the first six questions answered correctly and one point could be given for each of the last five, so there are 17 possible points. A percentage of those correct could be used.