1. Chapter Organizing and Summarizing Data © 2010 Pearson Prentice Hall. All rights reserved 3 2

2. Section 2.2 Organizing Quantitative Data: The Popular Displays Objectives 1.Organize discrete data in tables 2.Construct histograms of discrete data 3.Organize continuous data in tables 4.Construct histograms of continuous data 5.Draw stem-and-leaf plots 6.Draw dot plots 7.Identify the shape of a distribution © 2010 Pearson Prentice Hall. All rights reserved 2-2

3. The first step in summarizing quantitative data is to determine whether the data is discrete or continuous. If the data is discrete and there are relatively few different values of the variable, the categories of data will be the observations (as in qualitative data). If the data is discrete, but there are many different values of the variable, or if the data is continuous, the categories of data (called classes) must be created using intervals of numbers. © 2010 Pearson Prentice Hall. All rights reserved 2-3

4. Objective 1 Organize discrete data in tables © 2010 Pearson Prentice Hall. All rights reserved 2-4

5. EXAMPLE Constructing Frequency and Relative Frequency Distribution from Discrete Data The following data represent the number of available cars in a household based on a random sample of 50 households. Construct a frequency and relative frequency distribution. 3012111202422212202411324121223321220322232122113530121112024222122024113241212233212203222321221135 Data based on results reported by the United States Bureau of the Census. © 2010 Pearson Prentice Hall. All rights reserved 2-5

6. © 2010 Pearson Prentice Hall. All rights reserved 2-6

7. Objective 2 Construct histograms of discrete data © 2010 Pearson Prentice Hall. All rights reserved 2-7

8. A histogram is constructed by drawing rectangles for each class of data whose height is the frequency or relative frequency of the class. The width of each rectangle should be the same and they should touch each other. © 2010 Pearson Prentice Hall. All rights reserved 2-8

9. EXAMPLE Drawing a Histogram for Discrete Data Draw a frequency and relative frequency histogram for the “number of cars per household” data. © 2010 Pearson Prentice Hall. All rights reserved 2-9

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12. Objective 3 Organize continuous data in tables © 2010 Pearson Prentice Hall. All rights reserved 2-12

13. Categories of data are created for continuous data using intervals of numbers called classes. © 2010 Pearson Prentice Hall. All rights reserved 2-13

14. The following data represents the number of persons aged 25 - 64 who are currently work disabled. The lower class limit of a class is the smallest value within the class while the upper class limit of a class is the largest value within the class. The lower class limit of first class is 25. The lower class limit of the second class is 35. The upper class limit of the first class is 34. The class width is the difference between consecutive lower class limits. The class width of the data given above is 35 - 25 = 10. © 2010 Pearson Prentice Hall. All rights reserved 2-14

15. EXAMPLEOrganizing Continuous Data into a Frequency and Relative Frequency Distribution The following data represent the time between eruptions (in seconds) for a random sample of 45 eruptions at the Old Faithful Geyser in California. Construct a frequency and relative frequency distribution of the data. Source: Ladonna Hansen, Park Curator © 2010 Pearson Prentice Hall. All rights reserved 2-15

16. The smallest data value is 672 and the largest data value is 738. We will create the classes so that the lower class limit of the first class is 670 and the class width is 10 and obtain the following classes: © 2010 Pearson Prentice Hall. All rights reserved 2-16

17. The smallest data value is 672 and the largest data value is 738. We will create the classes so that the lower class limit of the first class is 670 and the class width is 10 and obtain the following classes: 670 - 679 680 - 689 690 - 699 700 - 709 710 - 719 720 - 729 730 - 739 © 2010 Pearson Prentice Hall. All rights reserved 2-17

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20. Objective 4 Construct histograms of continuous data © 2010 Pearson Prentice Hall. All rights reserved 2-20

21. EXAMPLE Constructing a Frequency and Relative Frequency Histogram for Continuous Data Using class width of 10: © 2010 Pearson Prentice Hall. All rights reserved 2-21

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23. Using class width of 5: © 2010 Pearson Prentice Hall. All rights reserved 2-23

24. Objective 5 Draw stem-and-leaf plots © 2010 Pearson Prentice Hall. All rights reserved 2-24

25. A stem-and-leaf plot uses digits to the left of the rightmost digit to form the stem. Each rightmost digit forms a leaf. For example, a data value of 147 would have 14 as the stem and 7 as the leaf. © 2010 Pearson Prentice Hall. All rights reserved 2-25

26. EXAMPLEConstructing a Stem-and-Leaf Plot An individual is considered to be unemployed if they do not have a job, but are actively seeking employment. The following data represent the unemployment rate in each of the fifty United States plus the District of Columbia in June, 2008. © 2010 Pearson Prentice Hall. All rights reserved 2-26

27. StateUnemployment Rate StateUnemployment Rate StateUnemployment Rate Alabama4.7Kentucky6.3North Dakota3.2 Alaska6.8Louisiana3.8Ohio6.6 Arizona4.8Maine5.3Oklahoma3.9 Arkansas5.0Maryland4.0Oregon5.5 California6.9Mass5.2Penn5.2 Colorado5.1Michigan8.5Rhode Island7.5 Conn5.4Minnesota5.3South Carolina6.2 Delaware4.2Mississippi6.9South Dakota2.8 Dist Col6.4Missouri5.7Tenn6.5 Florida5.5Montana4.1Texas4.4 Georgia5.7Nebraska3.3Utah3.2 Hawaii3.8Nevada6.4Vermont4.7 Idaho3.8New Hamp4.0Virginia4.0 Illinois6.8New Jersey5.3Washington5.5 Indiana5.8New Mexico3.9W. Virginia5.3 Iowa4.0New York5.3Wisconsin4.6 Kansas4.3North Carolina 6.0Wyoming3.2 © 2010 Pearson Prentice Hall. All rights reserved

28. We let the stem represent the integer portion of the number and the leaf will be the decimal portion. For example, the stem of Alabama will be 4 and the leaf will be 7. © 2010 Pearson Prentice Hall. All rights reserved 2-28

29. 2 8 3 888392922 4 782030104706 5 0145783237335253 6 89483940625 7 5 8 5 © 2010 Pearson Prentice Hall. All rights reserved 2-29

30. 2 8 3 222388899 4 000012346778 5 0122333334555778 6 02344568899 7 5 8 5 © 2010 Pearson Prentice Hall. All rights reserved 2-30

31. © 2010 Pearson Prentice Hall. All rights reserved 2-31

32. A split stem-and-leaf plot: 2 8 3 2223 3 88899 4 00001234 4 6778 5 0122333334 5 555778 6 02344 6 568899 7 7 5 8 8 5 This stem represents 3.0 – 3.4 This stem represents 3.5 – 3.9 © 2010 Pearson Prentice Hall. All rights reserved 2-32

33. Once a frequency distribution or histogram of continuous data is created, the raw data is lost (unless reported with the frequency distribution), however, the raw data can be retrieved from the stem-and-leaf plot. Advantage of Stem-and-Leaf Diagrams over Histograms © 2010 Pearson Prentice Hall. All rights reserved 2-33

34. Objective 6 Draw dot plots © 2010 Pearson Prentice Hall. All rights reserved 2-34

35. A dot plot is drawn by placing each observation horizontally in increasing order and placing a dot above the observation each time it is observed. © 2010 Pearson Prentice Hall. All rights reserved 2-35

36. EXAMPLE Drawing a Dot Plot The following data represent the number of available cars in a household based on a random sample of 50 households. Draw a dot plot of the data. 3012111202422212202411324121223321220322232122113530121112024222122024113241212233212203222321221135 Data based on results reported by the United States Bureau of the Census. © 2010 Pearson Prentice Hall. All rights reserved 2-36

37. © 2010 Pearson Prentice Hall. All rights reserved 2-37

38. Objective 7 Identify the shape of a distribution © 2010 Pearson Prentice Hall. All rights reserved 2-38

39. © 2010 Pearson Prentice Hall. All rights reserved 2-39

40. EXAMPLEIdentifying the Shape of the Distribution Identify the shape of the following histogram which represents the time between eruptions at Old Faithful. © 2010 Pearson Prentice Hall. All rights reserved 2-40

41. © 2010 Pearson Prentice Hall. All rights reserved 2-41