770 CHAPTER 12 Statistics You are creating a budget and decide to record the amount of money you spend weekly on food. After keeping a list of your weekly food expenses for many months, you realize you have a large set of data and want to condense your data into a more manageable form. In this section, we will learn a method to organize and summarize data. We will also introduce four types of graphs that can be used to display information in a meaningful way. Frequency Distributions and Statistical Graphs SECTION 12.2 LEARNING GOALS Upon completion of this section, you will be able to: 7 Construct frequency distributions. 7 Construct histograms and frequency polygons. 7 Construct stem-and-leaf displays. 7 Understand circle graphs. Why This Is Important Organizing and summarizing data and using graphs can make large sets of information more useful and help to determine important characteristics of the data. Frequency Distributions It is not uncommon for statisticians and others to have to analyze thousands of pieces of data. A piece of data is a single response to an experiment. The word data is plural. This means that the word data can represent either a single piece of data or a group of data. When the amount of data is large, it is usually advantageous to construct a frequency distribution. A frequency distribution is a listing of the observed values and the corresponding frequency of occurrence of each value. Example 1 shows how we construct a frequency distribution. America in 2000 and in 2050 White African American Hispanic* Asian and Pacific Islander American Indian, Eskimo and Aleut Source: Census.gov 12.2% 11.4% 0.7% 3.9% 24.5% 13.6% 0.9% 8.2% Projected population in 2050 394 million Population in 2000 275 million 71.8% 52.8% a) Compute the projected percent increase in population from 2000 to 2050 by using the formula given on page 587. 43.3% increase ≈ b) If the radius of the circle representing 2000 is 1 4 inch, compute the area of the circle. Use A r .2 π = Area 0.196 in.2 ≈ c) If the radius of the circle representing 2050 is 3 8 inch, compute the area of the circle. Area 0.442 in.2 ≈ d) Compute the percent increase in the size of the area of the circle from 2000 to 2050. 125.5% ≈ increase e) Are the circle graphs misleading? Yes Research Activities 45. Sampling Techniques Select one type of sampling technique and write a report on how statisticians obtain that type of sample. Also indicate when that type of sampling technique may be preferred. Describe two examples of when the sampling technique may be used. 46. Manipulating Statistics Read the book How to Lie with Statistics by Darrell Huff and write a book report on it. Select three illustrations from the book that show how people manipulate statistics.*See Instructor Answer Appendix 06photo/123RF
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