4 CHAPTER 1 Introduction to Statistics Two important terms that are used throughout this course are parameter and statistic. A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic. DEFINITION It is important to note that a sample statistic can differ from sample to sample, whereas a population parameter is constant for a population. For instance, consider the survey in Example 1. The results showed that 616 of 751 employees surveyed feel at least a little stressed at work. Another sample may have a different number of employees who say they feel at least a little stressed at work. For the population, however, the number of employees who feel at least a little stressed at work does not change. Distinguishing Between a Parameter and a Statistic Determine whether each number describes a population parameter or a sample statistic. Explain your reasoning. 1. In the United States, a survey of about 9400 individuals aged 15 and over found that such individuals spent an average of 5.19 hours per day engaged in leisure and sports activities. (Source: U.S. Bureau of Labor Statistics) 2. The freshman class at a university has an average SAT math score of 514. 3. In a random check of several hundred retail stores, the Food and Drug Administration found that 34% of the stores were not storing fish at the proper temperature. SOLUTION 1. Because the average of 5.19 hours per day is based on a subset of the population, it is a sample statistic. 2. Because the average SAT math score of 514 is based on the entire freshman class, it is a population parameter. 3. Because 34% is based on a subset of the population, it is a sample statistic. TRY IT YOURSELF 2 Determine whether each number describes a population parameter or a sample statistic. Explain your reasoning. a. Last year, a small company spent a total of $5,150,694 on employees’ salaries. b. In the United States, a survey of more than 1000 adults aged 65–80 found that 47% who report listening to loud or very loud music in their youth now report being hard of hearing. (Source: The Harris Poll) Answer: Page A35 In this course, you will see how the use of statistics can help you make informed decisions. Consider the census that the U.S. government takes every decade. The Census Bureau attempts to contact everyone living in the United States. Although it is impossible to count everyone, it is important that the census be as accurate as it can be because public officials make many decisions based on the census information. Data collected in the census will determine how to assign congressional seats and how to distribute public funds. Study Tip To remember the terms parameter and statistic, try using the mnemonic device of matching the first letters in population parameter and the first letters in sample statistic. Picturing the World What is the cost of the U.S. Census? According to estimates, it has been escalating with each decade.The cost of the 1950 Census was approximately $91.5 million. The most recent U.S. Census, taken in 2020, was estimated to cost a staggering $15.6 billion. (Source: U.S. Census Bureau and U.S. Government Accountability Office) 2 Year Cost (in billions of dollars) 1950 1960 1970 1980 1990 2000 2010 2020 4 6 8 10 12 14 16 U.S. Census Cost $0.0915 $0.1279 $0.2477 $1.1 $2.5 $4.5 $13.0 $15.6 What are some of the costs involved in taking a census? EXAMPLE 2
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