1. Copyright © Cengage Learning. All rights reserved.
Organizing Data 2
Copyright © Cengage Learning. All rights reserved.

2. Bar Graphs, Circle Graphs, and Time-Series Graphs
Section
2.2
Bar Graphs, Circle Graphs, and Time-Series Graphs
Copyright © Cengage Learning. All rights reserved.

3. Focus Points Determine types of graphs appropriate for specific data
Construct bar graphs, Pareto charts, circle graphs, and time-series graphs
Interpret information displayed in graphs

4. Feature of Bar Graphs Bars can be horizontal or vertical
The length of each bar represents the quantity to compare
Bars are of uniform width and are uniformly spaced
All graphs must be “stand-alone” entities
should be captioned, titled, and labeled to such an extent that no further explanation is needed
all axes must be appropriately scaled (numbered) and labeled
Larson/Farber 4th ed.

5. Example – Clustered Bar Graph, Two Categorical Variables
YEAR
Men
Woman
1980
70.0
77.4
1990
71.8
78.8
2000
73.0
79.7
2010
74.1
80.6 1
The decades are the cases. 2
The life expectancies are the frequency counts (in units of years) 3
The data is categorical (Man, Woman)
How are these two graphs compare?
Life Expectancy
Figure 2-11

6. Bar Graphs, Circle Graphs, and Time-Series Graphs
An important feature illustrated in Figure 2-11(b) is that of a changing scale. Notice that the scale between 0 and 65 is compressed.
The changing scale amplifies the apparent difference between life spans for men and women, as well as the increase in life spans from those born in 1980 to the projected span of those born in 2010.

7. Example: Misleading Graphs
Fig 2-1: one or both of the axes begin at some value other than zero, so that differences are exaggerated.

8. What Does This Chart Show?
A segmented (or stacked) bar chart displays the same information as a pie chart, but in the form of bars instead of circles.
Each bar is treated as the “whole” and is divided proportionally into segments corresponding to the percentage in each group.
Titanic Survivors: Here is the segmented bar chart for ticket Class by Survival status:

9. What is a Pareto Chart?
Frequency
Larson/Farber 4th ed.

10. Graphing Qualitative Data Sets
Pareto Chart
A vertical bar graph in which the height of each bar represents frequency or relative frequency.
The bars are positioned in order of decreasing height, with the tallest bar positioned at the left.
Frequency
Categories
Larson/Farber 4th ed.

11. Example: Constructing a Pareto Chart
In a recent year, the retail industry lost $41.0 million in inventory shrinkage. Inventory shrinkage is the loss of inventory through breakage, pilferage, shoplifting, and so on. The causes of the inventory shrinkage are administrative error ($7.8 million), employee theft ($15.6 million), shoplifting ($14.7 million), and vendor fraud ($2.9 million). Use a Pareto chart to organize this data. (Source: National Retail Federation and Center for Retailing Education, University of Florida)
Larson/Farber 4th ed.

12. Solution: Constructing a Pareto Chart
Cause
$ (million)
Admin. error
7.8
Employee theft
15.6
Shoplifting
14.7
Vendor fraud
2.9
From the graph, it is easy to see that the causes of inventory shrinkage that should be addressed first are employee theft and shoplifting.
Larson/Farber 4th ed.

13. Graphing Qualitative Data Sets
Pie Chart
A circle is divided into sectors that represent categories.
The area of each sector is proportional to the frequency of each category.
Larson/Farber 4th ed.

14. Example: Constructing a Pie Chart
The numbers of motor vehicle occupants killed in crashes in 2005 are shown in the table. Use a pie chart to organize the data. (Source: U.S. Department of Transportation, National Highway Traffic Safety Administration)
Vehicle type
Killed
Cars
18,440
Trucks
13,778
Motorcycles
4,553
Other
823
Larson/Farber 4th ed.

15. Solution: Constructing a Pie Chart
Find the relative frequency (percent) of each category.
Vehicle type
Frequency, f
Relative frequency
Cars
18,440
Trucks
13,778
Motorcycles
4,553
Other
823
37,594
Larson/Farber 4th ed.

16. Solution: Constructing a Pie Chart
Construct the pie chart using the central angle that corresponds to each category.
To find the central angle, multiply 360º by the category's relative frequency.
For example, the central angle for cars is
360(0.49) ≈ 176º
Larson/Farber 4th ed.

17. Solution: Constructing a Pie Chart
Vehicle type
Frequency, f
Relative frequency
Central angle
Cars
18,440
0.49
Trucks
13,778
0.37
Motorcycles
4,553
0.12
Other
823
0.02
360º(0.49)≈176º
360º(0.37)≈133º
360º(0.12)≈43º
360º(0.02)≈7º
Larson/Farber 4th ed.

18. Solution: Constructing a Pie Chart
Vehicle type
Relative frequency
Central angle
Cars
0.49
176º
Trucks
0.37
133º
Motorcycles
0.12
43º
Other
0.02 7º
From the pie chart, you can see that most fatalities in motor vehicle crashes were those involving the occupants of cars.
Larson/Farber 4th ed.

19. What is Shown By This Chart?
Larson/Farber 4th ed.

20. Graphing Paired Data Sets
Time Series
Data set is composed of quantitative entries taken at regular intervals over a period of time.
e.g., The amount of precipitation measured each day for one month.
Use a time series chart to graph.
time
Quantitative data
Larson/Farber 4th ed.

21. Exercise 1: Constructing a Time Series Chart
The table lists the number of cellular telephone subscribers (in millions) for the years 1995 through Construct a time series chart for the number of cellular subscribers. (Source: Cellular Telecommunication & Internet Association)
Larson/Farber 4th ed.

22. Solution: Constructing a Time Series Chart
Let the horizontal axis represent the years.
Let the vertical axis represent the number of subscribers (in millions).
Plot the paired data and connect them with line segments.
Larson/Farber 4th ed.

23. Solution: Constructing a Time Series Chart
The graph shows that the number of subscribers has been increasing since 1995, with greater increases recently.
Larson/Farber 4th ed.

24. Example: Constructing a Time Series Chart
Avg. Bill
  YEAR
(Dollars)
1995
51.00
1996
47.70
1997
42.78
1998
39.43
1999
41.24
2000
45.27
2001
47.37
2002
48.32
2003
49.99
2004
51.23
2005
54.30
The table lists the number of cellular telephone subscribers (in millions) for the years 1995 through Construct a time series chart for a subscriber’s average local monthly cellular bill. Note any patterns.
Larson/Farber 4th ed.

25. Example: Constructing a Time Series Chart
Can you describe/interpret the chart?
Larson/Farber 4th ed.

26. What is an Ogive?
Larson/Farber 4th ed.

27. What is an Ogive?
Larson/Farber 4th ed.

28. Section 2.2 Summary Graphed quantitative data using dot plots
Graphed qualitative data using pie charts and Pareto charts
Graphed paired data sets using time series charts
Larson/Farber 4th ed.

29. Stem-and-Leaf Displays
Section 2.3
Stem-and-Leaf Displays
Larson/Farber 4th ed.

30. Focus Points Construct a stem-and-leaf display from raw data
Use a stem-and-leaf display to visualize data distribution
Compare a stem-and-leaf display to a histogram

31. Exploratory Data Analysis
Exploratory Data Analysis (EDA) is an approach/philosophy for data analysis that employs a variety of techniques (mostly graphical) to
maximize insight into a data set
uncover underlying structure
detect outliers and anomalies

32. Can You Describe This Graph?
Larson/Farber 4th ed.

33. Graphing Quantitative Data Sets
Stem-and-leaf plot
Each number is separated into a stem and a leaf.
Similar to a histogram.
Still contains original data values. 26 2 3 4 5
Data: 21, 25, 25, 26, 27, 28, , 36, 36, 45
Larson/Farber 4th ed.

34. Example: Constructing a Stem-and-Leaf Plot
The following are the numbers of text messages sent last month by the cellular phone users on one floor of a college dormitory. Display the data in a stem-and-leaf plot.
Summer assignment contained a similar exercise.
Larson/Farber 4th ed.

35. Solution: Constructing a Stem-and-Leaf Plot
The data entries go from a low of 78 to a high of 159.
Use the rightmost digit as the leaf.
For instance,
7 | 8 = and 15 | 9 = 159
List the stems, 7 to 15, to the left of a vertical line.
For each data entry, list a leaf to the right of its stem.
Larson/Farber 4th ed.

36. Solution: Constructing a Stem-and-Leaf Plot
Include a key to identify the values of the data.
From the display, you can conclude that more than 50% of the cellular phone users sent between 110 and 130 text messages.
Larson/Farber 4th ed.

37. Back-To-Back Stemplot
Larson/Farber 4th ed.

38. Stem-and-Leaf Displays vs. Histograms
Stem-and-leaf displays show the distribution of a quantitative variable, like histograms, while preserving the individual values.
Stem-and-leaf displays contain all the information found in a histogram and, when carefully drawn, show the distribution.

39. Stem-and-Leaf vs. Histogram
Compare the histogram and stem-and-leaf display for the pulse rates of 24 women at a health clinic. Which graphical display do you prefer?

40. What Can Go Wrong?
Don’t make a histogram of a categorical variable—bar charts or pie charts should be used for categorical data.
Spaces in a histogram represent actual gaps in the data. Spaces indicate a region where there are no data values

41. What Can Go Wrong? (cont.)
Below is a badly drawn plot and the proper histogram for the number of juvenile bald eagles sighted in a collection of weeks:
Incorrect ! Correct!
Quantitative variable should be on the horizontal axis! Frequency counts should be the vertical scale. The bars on a histograms should be touching.

42. What Can Go Wrong? (cont.)
Choose a bin width appropriate to the data.
Changing the bin width changes the appearance of the histogram:

43. Unit Summary: Chapter 2 Type Advantages Comments Histogram
Provides excellent insight into the distribution of the data at a glance.
Not effective for some types of data. Unusual data values can result in displays very lacking in detail. A relative frequency histogram uses percent as the vertical axis instead of frequency. It will have the same shape as the frequency histogram.
Ogive
[ Cumulative Frequency Graph]
Makes it easy to describe the number of data entries that are equal to or below a certain data value.
Upper class boundaries are marked on the horizontal axis. Cumulative frequencies are marked on the vertical axis. Another type of ogive uses percent as the vertical axis instead of frequency.
Larson/Farber 4th ed.

44. Unit Summary: Chapter 2 Type Advantages Comments Dot Plot
Distribution of data is easy to see. Original data can be retrieved. Easy to spot extreme values.
Repeated data values are stacked.
Stem-and-Leaf Plot
Support for Exploratory Data Analysis (EDA). Convenient tool for organizing/sorting data.
Larson/Farber 4th ed.

45. Unit Summary: Chapter 2
Frequency Tables show how the data are distributed within classes
A histogram is a graphical display of the information in a frequency table
Bar graphs, Pareto charts, and pie charts are useful to show how quantitative or qualitative data are distributed over chosen categories
Time-series graphs show how data change over time
Stem-and-leaf displays are an effective means of ordering data and showing distribution features
Larson/Farber 4th ed.