Math Background

Lesson: Sampling Techniques
Introducing the Concept

The idea of selecting a sample that is representative of the population may be a new topic for your students. They will need to learn what a sample is and what makes a sample representative of a population.

Materials: posterboard

Preparation: Make a poster with the following information on it.

Sample 1 Since there are 1,000 voters in the school district, the school administration will call the parents of 100 of the students in the school and ask the parents if they support the building of an addition to the school.

Sample 2 The school administration will get a list of the 1,000 registered voters in the school district and randomly select 100 of them to ask whether they support building an addition to the school.

Sample 3 The school administration will get a list of 1,000 voters and select 15 of them to see if they support the building of an addition to the school.

  • Say: People often need to obtain information about a group that is very large—in fact, too large to ask. So they try to pick a sample that is representative of the population. Does anyone know what I mean by the word sample?
    Elicit from students that a sample is a subset of, or small group from, a larger group.
  • Say: If we wanted information about the average age of students in this school, it would be too difficult to ask everyone in school. So we might select a sample and ask them. What would be wrong with selecting just the students from our class?
    Students will probably say that they are not representative of all the students in the school. The students in the class are a lot older than those in lower grades or younger than those in higher grades.
  • Say: Picking this class as the sample would create a biased sample, because it would not be representative of the school as a whole.
    Discuss with students the meaning of the word biased.
  • Ask: What if we selected six students at random from all the students in the school: Would that make for a good sample? Why or why not?
    Students should say that the sample is probably too small to be representative of the school's population.
  • Say: One of the things you need to consider when selecting a sample is the size of the sample. Statisticians have sophisticated ways of selecting sample size that depend on what is being tested. In some situations they may use a sample equal to about one-tenth the total population. Since it is easy to find one-tenth of a number, we can use this approach for this activity. For example, if the population is 1,200, then our sample should be about 120.
  • Say: The population of our school is about 650 (or use your actual school population). If we selected 65 students at random, we would have a good sample from which to make some predictions. If we selected more students, it would make the predictions even more reliable.
  • Say: Let's say that a local school board wants to build an addition to its school. To see if it has support for such an addition, the board surveys voters in its school district. The board members are considering selecting the following samples.
    Point to the chart. Have a volunteer read each sample to the class.
  • Ask: Is Sample 1 a good sample?
    Students should say that the sample is biased because only families that have children in school will be asked about the addition. If they don't, explain why the sample is biased.
  • Ask: What do you think about Sample 2? Is it a good sample?
    Students will probably say that it is a good sample because all voters have an equal chance of being selected and the sample seems to be large enough to be representative of the total population.
  • Ask: Do you think Sample 3 is a good sample? Explain.
    Students should say that the sample is probably too small to be representative of the total population.

Houghton Mifflin Math Grade 6