2134–Groebner_Ch02_037-080 9/9/00 3:48 PM Page 37 CHAPTER 2 GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 2-1 FREQUENCY DISTRIBUTIONS AND HISTOGRAMS | 2-2 JOINT FREQUENCY DISTRIBUTIONS | 2-3 BAR CHARTS AND PIE CHARTS | 2-4 LINE CHARTS AND SCATTER DIAGRAMS | CHAPTER OUTCOMES After studying the material in Chapter 2, you should: 2-1: Be able to construct frequency distributions both manually and with your computer. 2-2: Be able to construct and interpret a frequency histogram. 2-3: Know how to construct and interpret various types of bar charts. 2-4: Understand the purpose of a Pareto chart and be able to construct one. 2-5: Be able to create a line chart and interpret the trend in the data. 2-6: Be able to construct and interpret a scatter plot. 2-7: Be able to develop and interpret joint frequency tables. 2134–Groebner_Ch02_037-080 9/9/00 3:48 PM Page 38 38 CHAPTER 2 Graphs,Charts,and Tables—Describing Your Data WHY YOU NEED TO KNOW Several years ago, a vice president for General Motors spoke at Not only will you be called on to actually do the data the University of Montana’s spring alumni and scholarship analysis necessary to make sense out of data, you also will banquet. After his speech, a student asked him what factor he find yourself on the receiving end of many statistical reports. considered to be the most important in his rise to the position Therefore, in addition to being able to perform the appropri- of vice president in one of the world’s largest companies. He ate data analysis, you also need to be able to question the responded that a short time after joining GM he took part in accuracy and validity of the charts, graphs, and analyses a presentation to a group of upper managers. Previously he received from others. had been taught the skills to effectively organize and present Business periodicals, such as Fortune and Business Week, complex data. His ability to translate the data into meaningful use graphs and charts extensively in conjunction with their information caught the attention of the company’s senior articles to help readers better understand key concepts. Many managers. A short time later, he was asked to coordinate advertisements will even use graphs and charts to effectively another presentation. He stated that he was certain that upper convey their messages. What better proof of the potential management remembered his presentations for their effective value of descriptive statistics than to observe ads costing display of business data. When management needed someone $50,000 or more per page using the concepts we will be dis- to lead a special project, he was selected. The success of that cussing in this text? project led to a significant promotion and the rest was history. This chapter introduces some of the most frequently Although you may not end up working at a company as used tools and techniques for describing data with graphs, large as General Motors, we are absolutely convinced that you charts, and tables. Although all this analysis can be done man- will have numerous opportunities to organize, summarize, ually, we will provide output from Excel and Minitab showing analyze, and present data. In fact, of all the tools and tech- that these software packages can be used as tools for doing the niques introduced in this text, you will very likely use those analysis easily, quickly, and with a finished quality that once discussed in this chapter and Chapter 3 more than any other. required a graphic artist. I 2-1: FREQUENCY DISTRIBUTIONS AND HISTOGRAMS Next time you are in your statistics class look around at your classmates. How many hours a week do they spend studying? How are the ages of the students in the class distributed? How is income distributed among the students in the class? How many credits have they completed already? A simple survey of the students would provide data to answer each of these questions. However, the data alone would not be enough. You would need to perform a descriptive analysis of the data. One of the first steps in the analysis would be to construct a frequency distribution for each of the variables. FREQUENCY DISTRIBUTION A summary of a set of data that displays the number of observations in each of the distribu- tion’s distinct categories or classes. Frequency Distributions Books and Music Consider an example involving a national book and music retailer that is considering locat- 2-1 ing into one of two cities (say, City #1 and City #2). To obtain data to aid in the decision process, the retailer has conducted a marketing study in the two cities. Among the ques- FREQUENCY DISTRIBUTION tions asked of individuals is how many years of college they have completed. Experience in other markets indicates that cities with higher-educated populations are more profitable 2134–Groebner_Ch02_037-080 9/9/00 3:48 PM Page 39 2-1: Frequency Distributions and Histograms 39 TABLE 2-1 TABLE 2-2 Frequency Distribution of Years of College Frequency Distribution of Years of College CITY #1 CITY #2 YEARS OF COLLEGE FREQUENCY YEARS OF COLLEGE FREQUENCY 0350 187 121162 224234 322319 431414 51357 6663 7574 83 Total 330 Total 160 locations. The variable, years of college, is discrete since the possible responses (1, 2, 3, 4, etc.) can be counted. DISCRETE DATA Data whose possible values are countable. To construct the frequency distribution for City #1, we need only count the number of times individuals in that city indicate each of these possible responses (years of education). The results are shown in Table 2-1. This frequency distribution shows that, of the 160 people in the survey, most (125 out of 160) have spent at least one year in college. Suppose now we wished to compare the college years variable for City #1 with the same variable for City #2. The data for City #2 can be organized into the frequency distri- bution shown in Table 2-2. How do the two market areas compare? Do you see any difficulties in making this comparison? Since the surveys contained a different number of people, the frequencies of each category are difficult to compare directly. When the number of total observations dif- fers, comparisons are aided if relative frequencies are computed. Equation 2-1 is used to compute the relative frequencies. Table 2-3 shows the relative frequencies for each market area. This makes a comparison of the two market areas much easier. We see that City #2 has relatively more people without any college education (56.7%) or one year of college (18.8%) than City #1 (21.9% and 13.1%). At all other levels of education, City #1 has relatively more people than does City #2. RELATIVE FREQUENCY The proportion of total observations contained in a given category. Relative frequency is com- puted by dividing the frequency in a category by the total number of observations. The relative frequencies can be converted to percents by multiplying by 100. f RF ϭ ᎏi 2-1 n where: ϭ fi frequency of the ith value of the discrete variable k ϭ n Α fi iϭ1 k ϭ the number of different values for the discrete variable 2134–Groebner_Ch02_037-080 9/9/00 3:48 PM Page 40 40 CHAPTER 2 Graphs,Charts,and Tables—Describing Your Data CITY #1 CITY #2 Years of College Frequency Relative Frequency Frequency Relative Frequency 0 35 35/160 ϭ 0.219 187 187/330 ϭ 0.567 1 21 21/160 ϭ 0.131 62 62/330 ϭ 0.188 2 24 24/160 ϭ 0.150 34 34/330 ϭ 0.103 3 22 22/160 ϭ 0.138 19 19/330 ϭ 0.058 4 31 31/160 ϭ 0.194 14 14/330 ϭ 0.042 5 13 13/160 ϭ 0.081 7 7/330 ϭ 0.021 6 6 6/160 ϭ 0.038 3 3/330 ϭ 0.009 TABLE 2-3 7 5 5/160 ϭ 0.031 4 4/330 ϭ 0.012 Relative Frequency 8 3 3/160 ϭ 0.019 0 0/330 ϭ 0 Distribution for the Book and Total 160 330 Music Example Weigh-in-Motion Examine the contents of the room you presently occupy. Think about all the items in your 2-2 home. Chances are these things were transported by truck. Trucks play an important role in our transportation system. However, trucks adversely impact the roads and highways over FREQUENCY DISTRIBUTION which they travel. The more weight on each axle, the more damage done to the pavement. To help states compensate for this wear, truckers are charged a tax for the privilege of using the roads and highways. In many states, this tax is based on the weight of the truck and the number of miles driven—the tax is called a ton-mile tax. In order to know how much tax to assess, trucks must be weighed and mileage read- Excel and Minitab ings must be made. Ports of Entry (POE) are placed at strategic locations throughout the Tutorial state. Trucks are required to pull into the POE to be weighed and measured. This is a time- consuming, labor-intensive process when the old-style platform scales are used. The trucks must actually stop on the scale while the weight on each axle is recorded. These scales are assumed to be accurate. In recent years, new technology has emerged for weighing trucks. This technology is called weigh-in-motion or WIM.