Populations, Samples, and Variables Study Guide
Introduction to Populations, Samples, and Variables
Numerical information permeates our lives. The morning weather report forecasts the chance of rain, and we make a decision as to whether or not to take an umbrella. Given the latest study results on the health risks of over-the-counter painkillers, we decide whether take something to reduce the pain from a sore knee. A friend wants to attend a very selective university and wonders whether an SAT score of 1,400 or higher will ensure her admittance. A neighbor was told that there was a peculiar shadow on an X-ray and must decide whether to have a biopsy taken. The stock market has had several days of losses, and an investor wonders whether this trend will continue. Our understanding of these and many other issues will be deeper as we learn more about the discipline of statistics. But what is statistics? Learning the answer to this question, as well as some fundamental terms in statistics, such as population, sample, and variable, is the focus of this lesson.
Populations and Samples
Statistics is the science of collecting, analyzing, and drawing conclusions from data. This process of collecting, analyzing, and drawing conclusions begins with the desire to answer a question about a specific population. In statistics, a population is the collection of individuals or objects of interest. These individuals or objects may be referred to as members or units of the population. If we are able to record all desired information on each unit in the population, then we have taken a census. The problem is that we rarely have the ability to gather the information from every unit of the population, due to financial constraints, time limitations, or some other reason. We must be satisfied with observing the information for only a sample, or a subset of the population of interest.
Care must be taken in obtaining the sample if we are to be able to draw solid conclusions from it. For example, if we are interested in whether a majority of the voters in a particular state would favor increasing the minimum driving age, then we would not want to simply call several households and ask the person answering the phone whether he or she favored increasing the minimum driving age. In households with children, the children are more likely to answer the phones than the adults, and the views of these nonvoters might be quite different from their voting parents. Deciding how to select the sample from the population is an important aspect of data collection.
A proposal before a state's legislature would increase the gasoline tax. The additional funds would be used to improve the state's roads. Some state legislators are concerned about how the voters view this proposal. To gain this information, a pollster randomly selects 1,009 registered voters in the state and asks each whether or not he or she favors the additional tax for the designated purpose. Describe the population and sample.
The population is all registered voters in the state. The sample is made up of the 1,009 registered voters who were polled.