SECTION 1.1 An Overview of Statistics 5 Branches of Statistics The study of statistics has two major branches: descriptive statistics and inferential statistics. Descriptive statistics is the branch of statistics that involves the organization, summarization, and display of data. Inferential statistics is the branch of statistics that involves using a sample to draw conclusions about a population. A basic tool in the study of inferential statistics is probability. (You will learn more about probability in Chapter 3.) DEFINITION Descriptive and Inferential Statistics For each study, identify the population and the sample. Then determine which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics? 1. A study of 1502 U.S. adults found that 18% of adults from households earning less than $30,000 annually do not use the Internet, as shown in the figure at the left. (Source: Pew Research Center) 2. A study of 1000 U.S. 401(k) retirement plan participants found that the percentage who do not know how many years their retirement savings might last is 32%. (Source: Charles Schwab & Co., Inc.) SOLUTION 1. The population consists of the responses of all U.S. adults, and the sample consists of the responses of the 1502 U.S. adults in the study. The part of this study that represents the descriptive branch of statistics involves the statement “18% of adults from households earning less than $30,000 annually do not use the Internet.” Also, the figure represents the descriptive branch of statistics. A possible inference drawn from the study is that the Internet has been made inaccessible to lower-income households. 2. The population consists of the responses of all U.S. 401(k) retirement plan participants, and the sample consists of the responses of the 1000 U.S. 401(k) retirement plan participants in the study. The part of this study that represents the descriptive branch of statistics involves the statement “the percentage [of U.S. 401(k) retirement plan participants] who do not know how many years their retirement savings might last is 32%.” A possible inference drawn from the study is that the amount of money a person needs for retirement is difficult to determine. TRY IT YOURSELF 3 A study of 513 respondents to an Internet-wide survey found that 97% of the respondents said music is important to them, and 83% of the respondents said they actively look for new music. (Source: Medium) a. Identify the population and the sample. b. Determine which part of the study represents the descriptive branch of statistics. c. What conclusions might be drawn from the study using inferential statistics? Answer: Page A35 EXAMPLE 3 Household income U.S. adults who do not use the Internet by household income Not Online Less than $30,000 18% 7% 3% 2% $75,000 or more $30,000 to $49,999 $50,000 to $74,999 Study Tip Throughout this course you will see applications of both branches of statistics. A major theme in this course will be how to use sample statistics to make inferences about unknown population parameters.
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