1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 2.2 Graphical Displays of Data

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Create and interpret the basic types of graphs used to display data. o Distinguish between the basic shapes of a distribution.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.7: Creating a Pie Chart Create a pie chart from the following data describing the distribution of housing types for students in a statistics class. Calculate the size of each wedge in the pie chart to the nearest whole degree. Housing Types for Students in a Statistics Class Type of HousingNumber of Students Apartment Dorm House Sorority/Fraternity House 20 15 9 5 Total49

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.7: Creating a Pie Chart (cont.) Solution Relative Frequencies Central Angle Measures

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.7: Creating a Pie Chart (cont.)

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.8: Creating a Bar Graph Create a bar graph of the following data describing the distribution of housing types for students in a statistics class. Housing Types for Students in a Statistics Class Type of HousingNumber of Students Apartment Dorm House Sorority/Fraternity House 20 15 9 5

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.8: Creating a Bar Graph (cont.) Solution

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.9: Creating a Pareto Chart Create a Pareto chart, if appropriate, for the following data. Fundraising Results ClassNumber of Fundraiser items sold Ms. Boyd’s class Ms. Willard’s class Ms. Smith’s class Ms. Carter’s class Ms. Meredith’s class 200 157 176 181 143

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.9: Creating a Pareto Chart (cont.) Solution The data are nominal; therefore, it would be appropriate to create a Pareto chart from these data. Begin by rearranging the data from the largest frequency to the smallest frequency. Ordered Fundraising Results ClassNumber of Fundraiser items sold Ms. Boyd’s class Ms. Carter’s class Ms. Smith’s class Ms. Willard’s class Ms. Meredith’s class 200 181 176 157 143

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.9: Creating a Pareto Chart (cont.) Next, create a bar graph of the ordered data. The resulting Pareto chart is shown.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.10: Creating a Side-by-Side Bar Graph Create a side-by-side bar graph of the following data describing the distribution of housing types for two different samples of students. Housing Types for Students in a Statistics Class Type of HousingNumber of Students from Sample A Number of Students from Sample B Apartment Dorm House Sorority/Fraternity House 20 15 9 5 13 24 6 7

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.10: Creating a Side-by-Side Bar Graph (cont.) Solution

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.11: Creating a Stacked Bar Graph Create a stacked bar graph for the data in Example 2.10. Solution With the stacked bar graph, it is easier to see that more students live in the dorms than in apartments.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.12: Constructing a Histogram Construct a histogram of the 3-D TV prices from the previous section. The frequency distribution of the data is restated here. 3-D TV Prices ClassFrequencyMidpointClass Boundaries $1500 - $1599 $1600 - $1699 $1700 - $1799 $1800 - $1899 $1900 - $1999 2545425454 1549.5 1649.5 1749.5 1849.5 1949.5 1499.5 – 1599.5 1599.5 – 1699.5 1699.5 – 1799.5 1799.5 – 1899.5 1899.5 – 1999.5

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.12: Constructing a Histogram (cont.) Solution

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.12: Constructing a Histogram (cont.)

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.13: Constructing a Relative Frequency Histogram Construct a relative frequency histogram of the 3-D TV prices from the previous section. The frequency distribution of the data is reprinted here. 3-D TV Prices ClassFrequencyRelative Frequency $1500 - $1599 $1600 - $1699 $1700 - $1799 254254

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.13: Constructing a Relative Frequency Histogram (cont.) 3-D TV Prices (cont.) ClassFrequencyRelative Frequency $1800 - $1899 $1900 - $1999 5454

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.13: Constructing a Relative Frequency Histogram (cont.) Solution

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Frequency Polygons Constructing a Frequency Polygon 1.Mark the class boundaries on the x ‑ axis and the frequencies on the y ‑ axis. Note, extra classes at the lower and upper ends will be added, each having a frequency of 0. In our 3-D TV price example, these classes will be 1400–1499 at the lower end and 2000–2099 at the upper end.

21. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Frequency Polygons Constructing a Frequency Polygon (cont.) 2.Add the midpoints to the x-axis and plot a point at the frequency of each class directly above its midpoint. Notice that the class boundaries on the x ‑ axis have been lightened. This is due to the fact that frequency polygons represent the midpoints of the classes.

22. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Frequency Polygons Constructing a Frequency Polygon (cont.) 3.Join each point to the next with a line segment. Notice, this is not a smooth curve, but a polygon.

23. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.14: Creating an Ogive Below is the frequency distribution of the 3-D TV prices with the cumulative frequency column included. Create an ogive of the data.

24. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.14: Creating an Ogive (cont.) 3-D TV Prices ClassFrequencyCumulative Frequency Class Boundaries $1400 - $1499 $1500 - $1599 $1600 - $1699 $1700 - $1799 $1800 - $1899 $1900 - $1999 025454025454 0 2 7 11 16 20 1399.5 – 1499.5 1499.5 – 1599.5 1599.5 – 1699.5 1699.5 – 1799.5 1799.5 – 1899.5 1899.5 – 1999.5

25. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.14: Creating an Ogive (cont.) Solution Notice we have included the class 1400–1499 with a frequency of 0. The following is an ogive of the data.

26. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Stem-and-Leaf Plots Constructing a Stem ‑ and-Leaf Plot 1.Create two columns, one on the left for stems and one on the right for leaves. 2.List each stem that occurs in the data set in numerical order. Each stem is normally listed only once; however, the stems are sometimes listed two or more times if splitting the leaves would make the data set’s features clearer.

27. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Stem-and-Leaf Plots Constructing a Stem ‑ and-Leaf Plot (cont.) 3.List each leaf next to its stem. Each leaf will be listed as many times as it occurs in the original data set. There should be as many leaves as there are data values. Be sure to line up the leaves in straight columns so that the table is visually accurate. 4.Create a key to guide interpretation of the stem ‑ and-leaf plot. 5.If desired, put the leaves in numerical order to create an ordered stem-and-leaf plot.

28. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.15: Creating a Stem-and-Leaf Plot Create a stem-and-leaf plot of the following ACT scores from a group of college freshmen. ACT Scores 18 27 35 18 23 26 27 17 24 22 29 21 31 32 24 25 19 18 20 26

29. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.15: Creating a Stem-and-Leaf Plot (cont.) Solution ACT Scores Stem Leaves 123123 8 9 8 8 7 3 4 7 6 2 7 9 4 0 1 5 6 1 2 5 Key: 1|8 = 18

30. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.16: Creating and Interpreting a Stem- and-Leaf Plot Create a stem-and-leaf plot for the following starting salaries for entry-level accountants at public accounting firms. Use the stem-and-leaf plot that you create to answer the following questions. Starting Salaries for Entry-Level Accountants $51,500 $45,500 $45,800 $43,000 $42,900 $44,500 $48,300 $42,500 $46,300 $42,700 $46,500 $47,900 $40,900 $44,200 $50,000 $49,000 $47,700 $45,300 $40,700 $46,400 $50,700 $46,700 $48,000 $46,100 $48,200 $48,600 $44,300 $43,200 $46,300 $45,000

31. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.16: Creating and Interpreting a Stem- and-Leaf Plot (cont.) a.What were the smallest and largest salaries recorded? b.Which salary appears the most often? c.How many salaries were in the range $41,000 – $41,900? d.In which salary range did the most salaries lie: $40,000–$44,900, $45,000–$49,900, or $50,000 and above?

32. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.16: Creating and Interpreting a Stem- and-Leaf Plot (cont.) Solution This example is different than Example 2.15 in that the data have more than two digits and every data value ends in two zeros. It is important to choose the stems of the numbers so that the last significant digit in each data point will be the leaf in the chart. Listing the zeros as the leaves for each different stem would be of little use to anyone interpreting the stem-and-leaf plot. Instead, the key will denote that the salaries listed are in hundreds.

33. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.16: Creating and Interpreting a Stem- and-Leaf Plot (cont.) Using the first two digits of each salary as a stem, we have the following plot. (Note: It is helpful to first list the salaries in numerical order.)

34. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.16: Creating and Interpreting a Stem- and-Leaf Plot (cont.)

35. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.16: Creating and Interpreting a Stem- and-Leaf Plot (cont.) a.The smallest salary is $40,700; the largest salary is $51,500. b.$46,300 appears twice, which is more than any other salary. c.No salaries are in the range $41,000–$41,900 because there are no leaves listed for the stem 41. d.By counting the leaves in the given groups, we see that there are more salaries in the range $45,000– $49,900.

36. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.17: Constructing a Line Graph The Consumer Price Index (CPI) is a measure of the average change in value over time for a basket of goods and services. It is an index calculated by the US Bureau of Labor and Statistics. The table below shows the values of the CPI from several years. Construct a line graph of these data.

37. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.17: Constructing a Line Graph (cont.) Consumer Price Index YearCPI 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 20.0 16.7 14.0 24.1 29.6 38.8 82.4 130.7 172.2 218.1 Source: US Bureau of Labor Statistics. “Consumer Price Index History Table.” 19 Jan. 2012. ftp://ftp.bls.gov/pub/special.req uests/cpi/cpiai.txt (24 Jan. 2012).

38. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.17: Constructing a Line Graph (cont.) Solution

39. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Summary Type of GraphDefinition Pie Chart Bar Graph A pie chart shows how large each category is in relation to the whole; that is, it uses the relative frequencies from the frequency distribution to divide the “pie” into different-sized wedges. It can only be used to display qualitative data. In a bar graph, bars are used to represent the amount of data in each category; one axis displays the categories of qualitative data and the other axis displays the frequencies. Qualitative Data

40. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Summary (cont.) Type of GraphDefinition Pareto Chart Side-by-Side Bar Graph A Pareto chart is a bar graph with the bars in descending order of frequency. Pareto charts are typically used with nominal data. A side-by-side bar graph is a bar graph that compares the same categories for different groups. Qualitative Data (cont.)

41. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Summary (cont.) Type of GraphDefinition Stacked Bar Graph A stacked bar graph is a bar graph that compares the same categories for different groups and shows category totals. Qualitative Data (cont.)

42. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Summary (cont.) Quantitative Data Type of GraphDefinition Histogram Frequency Polygon A histogram is a bar graph of a frequency distribution of quantitative data; the horizontal axis is a number line. A frequency polygon is a visual display of the frequency of each class of quantitative data that uses straight lines to connect points plotted above the class midpoints.

43. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Summary (cont.) Type of GraphDefinition Ogive Stem-and-Leaf Plot An ogive displays the cumulative frequency of each class of quantitative data by using straight lines to connect points plotted above the upper class boundaries. A stem-and-leaf plot retains the original data; the leaves are the last significant digit in each data value and the stems are the remaining digits. Quantitative Data (cont.) Stem Leaves 32 33 34 0 7 7 7 8 0 0

44. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Summary (cont.) Type of GraphDefinition Dot Plot Line Graph A dot plot retains the original data by plotting a dot above each data value on a number line. A line graph uses straight lines to connect points plotted at the value of each measurement above the time it was taken. Quantitative Data (cont.)