Introducing the Concept
The idea of choosing a sample which is representative of the population is a new topic for your students. They will need to acquire an understanding of what a sample is and the need for the sample to be representative of the population.
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 100 parents of students in school and ask them if they support building an addition on the school.
Sample 2: The school administration will get the list of the 1,000 registered voters and randomly select 100 of them to see if they support building an addition on the school.
Sample 3: The school administration will get the list of 1,000 voters and select 15 of them to see if they support the building of an addition on the school.
- Say: Many times people may want to obtain information about a group which is very large, in fact, too large to ask everyone. So, they try to pick a sample which is representative of the population. Does anyone know what I mean by the word "sample?"
Elicit from students that a sample is a subset or small group from a larger group.
- Say: If we wanted to find out information about the average age of students in this school, it would be a lot of work to make sure we asked everyone in school. So we might select a sample and ask them the question. What would be wrong with selecting just the students from this class?
Students will probably say that the students in this class would not be representative of all the students in the school. The students in the class would be a lot older than those in lower grades or younger than students 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'.) 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 will say that the sample is probably too small to be representative of the whole population.
- Say: One of the things you need to consider when picking a sample is the size of the sample. Statisticians have sophisticated ways of selecting sample size. One general rule they use is to pick a sample equal to about one tenth of the total number in the total population. For example, if the size of the population is 1,200, then we would select a sample of about 120.
- Say: The population of our school is about 650 (or your actual school population). If we select 65 students at random, we would have a good sample from which to make some predictions. If we picked 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 a school. To see if they have support for such an addition, they want to survey voters in their school district. They are considering selecting the following samples.
Point to the chart. Have a volunteer read each sample to the class.
- Ask: What do you think about sample 1?
Students will probably 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 this 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, since 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 will probably say that the sample is too small to be representative of the population.
Measures of Central Tendency:
Mean, Median, and Mode