SECTION 1.1 An Overview of Statistics 3 Data Sets There are two types of data sets you will use when studying statistics. These data sets are called populations and samples. A population is the collection of all outcomes, responses, measurements, or counts that are of interest. A sample is a subset, or part, of a population. DEFINITION A sample is used to gain information about a population. For instance, to estimate the unemployment rate for the population of the United States, the U.S. Bureau of Labor Statistics uses a sample of about 60,000 households. A sample should be representative of a population so that sample data can be used to draw conclusions about that population. Sample data must be collected using an appropriate method, such as random sampling. When sample data are collected using an inappropriate method, the data cannot be used to draw conclusions about the population. (You will learn more about random sampling and data collection in Section 1.3.) Identifying Data Sets In a survey, 751 employees in the United States were asked how stressed they feel at work. Of the 751 respondents, 616 said that they feel at least a little stressed at work. Identify the population and the sample. Describe the sample data set. (Adapted from The Marlin Company) SOLUTION The population consists of the responses of all employees in the United States. The sample consists of the responses of the 751 employees in the survey. In the Venn diagram below, notice that the sample is a subset of the responses of all employees in the United States. Also, the sample data set consists of 616 employees who said that they feel at least a little stressed at work and 135 who said that they do not feel stressed at work. Responses of employees in survey (sample) Responses of employees not in the survey Responses of All Employees (population) TRY IT YOURSELF 1 In a survey of 1516 teens in the United States, 1228 said “mental health is a significant issue for young people in the U.S.” Identify the population and the sample. Describe the sample data set. (Adapted from National 4-H Council) Answer: Page A35 Whether a data set is a population or a sample usually depends on the context of the real-life situation. For instance, in Example 1, the population is the set of responses of all employees in the United States. Depending on the purpose of the survey, the population could have been the set of responses of all employees who live in California or who work in the health care industry. EXAMPLE 1 Study Tip A census consists of data from an entire population. But, unless a population is small, it is usually impractical to obtain all the population data. In most studies, information must be obtained from a random sample.
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