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Learning Math Home
Session 1 Part A Part B Part C Part D Homework
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Session 1 Materials:

Session 1, Part D:
Bias in Sampling (20 minutes)

In This Part: Population and Sample | Random Sampling

In data analysis, we use graphs, tables, and numerical summaries to study the variation present in our data. Often, we want to extend our interpretation to a larger group beyond the particular group studied. Such generalizations are only valid, however, if the data we examine are representative of that larger group. If not, our interpretation may misrepresent the larger group! Note 4

The entire group that we want information about is called the population. We can gain information about this group by examining a portion of the population, called a sample.

To gain useful information, the sample must be representative of the population. A representative sample is one in which the relevant characteristics of the sample members are generally the same as the characteristics of the population.

There are several good reasons that we use samples to study populations; chief among them are feasibility and cost. For instance, in a nationwide political survey of the population of all voters in the United States, it would be difficult, if not impossible, to poll every voter. It would also be quite expensive. Statistical theory shows that a survey of a 1,000 carefully selected voters suffices to represent the opinions of the millions of people in the population of voters.

Another problem in answering questions about a population arises when we want to inspect or test products. For example, testing an air bag to see if it works properly means that we have to destroy it. We certainly can't test every air bag, but testing a carefully selected sample of air bags will tell us what we need to know about all the air bags in the population.

Problem D1


Think of a statistical question and a population. How could you determine a representative sample of that population? What would be a sample that is not representative?

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
A population might be the students at a certain school, the members of the Republican party, or all the soda cans shipped to the nearest convenience store this year. A representative sample must have all the same characteristics as the population.   Close Tip


How we select a sample is extremely important. Improper or biased sample selection can produce misleading conclusions. Sample selection is biased if it systematically favors certain outcomes. If we select only Democrats to participate in a political survey, the outcome will reflect Democrats' opinions, but not other political parties'. If we personally select a sample of students we know and like for a school survey, we have just eliminated the differing opinions of those whom we do not know and like. We need to select our sample in an unbiased fashion.

Next > Part D (Continued): Random Sampling

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