1. Copyright © 2008 Pearson Education, Inc.

2. Chapter 2 Organizing Data
Section 2.3
Graphs and Charts

3. The Role of Graphs
The purpose of graphs in statistics is to convey the data to the viewer in pictorial form.
Graphs are useful in getting the audience’s attention in a publication or a presentation.

4. Three Most Common Graphs
Histogram, Cumulative Frequency, Frequency Polygon
The histogram displays the data by using contiguous vertical bars of various heights to represent the frequencies of the classes.

5. Frequency and Relative-Frequency Histograms
Frequency histogram: A graph that displays the classes
on the horizontal axis and the frequencies of the classes
on the vertical axis. The frequency of each class is
represented by a vertical bar whose height is equal to the
frequency of the class.
Change to page 72

6. Relative Frequency Graphs
A relative frequency histogram is a graph that uses proportions instead of frequencies. Relative frequencies are used when the proportion of data values that fall into a given class is more important than the actual number of data values that fall into that class (frequency).
A relative frequency histogram displays the classes on the horizontal axis and the relative frequencies of the classes on the vertical axis.
The relative frequency of each class is represented by a vertical bar whose height is equal to the relative frequency of the class.

7. Cereal Calories
130
190
140 80
100
120
220
110
210 90
200
180
260
270
160
240
115
225
The number of calories per serving for selected ready-to-eat cereals is listed here. Construct a frequency distribution using 7 classes. Draw a histogram for the data. Describe the shape of the histogram.

8. Cereal Calories Width = 29 (rule 2) High = 270 Low = 80
Range = 270 – 80 = 190
Width = 190 ÷ 7 = 27.1 or 28
Width = 29 (rule 2)

9. Cereal Calories Limits Boundaries F RF CRF 80-108 79.5-108.5 8
08/46=0.17
0.17 13
13/46=0.28
0.45 2
02/46=0.04
0.49 9
09/46=0.20
0.69 10
10/46=0.22
0.91
0.95
0.99* 46
*0.99
*due to rounding not 100%

10. Cereal Calories
Histogram

11. Example 2.10
The table shows frequency and relative-frequency distributions for the days-to-maturity data. Obtain graphical displays for these grouped data.
Changed to page 58
Table 2.12

12. Solution Example 2.10
One way to display these grouped data pictorially is to construct a graph, called a frequency histogram, that depicts the classes on the horizontal axis and the frequencies on the vertical axis.
Move Page 59, Figure 2.2 to Slide 15
Insert Page 59 Definition 2.4 this slide 16
Figure 2.2

13. Scatter Plots or Dotplots
A scatter plot or dotplots are graphs of ordered pairs of data values that are used to determine if a relationship exists between the two variables.
Typically, the independent variable is plotted on the x-axis and the dependent variable is plotted on the y-axis.
When data is collected in pairs, the relationship, if one exists, can be determined by looking at a scatter plot

14. Paired Data and Scatter Plots
Many times researchers are interested in determining if a relationship between two variables exist.
To do this, the researcher collects data consisting of two measures that are paired with each other.
The variable first mentioned is called the independent variable (x); the second variable is the dependent variable (y).
Once you have an ordered pair ( x, y ) a graph can be drawn to represent the data.

15. Analyzing a Scatter Plot
A positive linear relationship exists when the points fall approximately in an ascending straight line and both the x and y values increase (left to right) at the same time. The relationship is that the values for x variable increases and values for y variable are increasing

16. Analyzing a Scatter Plot
A negative linear relationship exists when the points fall approximately in a straight line descending from left to right. The relationship then is that values for x are increasing and values for y values decreasing or vice versa.

17. Analyzing a Scatter Plot
A nonlinear relationship exists when the points fall along a curve. The relationship is described buy the nature of the curve.
No relationship exists when there is no discernable pattern of the points.

18. Example 2.12
One of Professor Weiss’s sons wanted to add a new DVD player to his home theater system. He used the Internet to shop and went to pricewatch.com. There he found 16 quotes on different brands and styles of DVD players. Construct a dotplot for these data.
Change to page 61
Insert Table 2.14 alongside figure 2.4
Table 2.14

19. Example - Employee Absences
Employee Absences: A researcher wishes to determine if there is a relationship between the number of days an employee missed a year and the person’s age. Draw a scatter plot and comment on the nature of the relationship.
AGE (X)
DAYS MISSED (Y) 22 30 4 25 1 35 2 65 14 50 7 27 3 53 8 42 6 58

20. Answer - Employee Absences
AGE (X)
DAYS MISSED (Y) 22 30 4 25 1 35 2 65 14 50 7 27 3 53 8 42 6 58
There appears to be a positive linear relationship
between an employee’s age and the number or days
missed per year.

21. Solution Example 2.12
Dotplot is another type of graphical display for quantitative data. To construct a dotplot for the data, we begin by drawing a horizontal axis that displays the possible prices. Then we record each price by placing a dot over the appropriate value on the horizontal axis. For instance, the first price is $210, which calls for a dot over the “210” on the horizontal axis.
Change to page 61
Insert Table 2.14 alongside figure 2.4
Figure 2.4

22. Stem-and-Leaf Plots
A stem-and-leaf plot is a data plot that uses part of a data value as the stem and part of the data value as the leaf to form groups or classes. Also known as stem-and-leaf diagram and stemplot.
It has the advantage over grouped frequency distribution of retaining the actual data while showing them in graphic form.
Stem-and-leaf diagrams is one of an arsenal of staticaa tools know as exploratory data analysis.

23. Presidents’ Ages at Inauguration
Presidents’ ages at inauguration – The age of each U.S. President is shown. Construct a stem and leaf plot and analyze the data. 57 61 55 58 54 68 51 49 64 48 65 52 56 46 50 47 42 60 62 43 69

24. Presidents’ Ages at Inauguration
Step 1: Arrange the data in order
Step 2: Separate the data according to classes.
40-45; 46-49; 50-55; 56-59; 60-65; 66-69
Step 3: Plot
Step 4: Analyze
4 2 3
The distribution is somewhat symmetric and unimodal. The majority of the Presidents were in their 50’swhen inaugurated.

25. Solution Example 2.13
For Table 2.15, repeats the data on the number of days to maturity for 40 short-term investments…Let’s construct a stem-and-leaf diagram, which simultaneously groups the data and provides a graphical display similar to a histogram.
Change to page 68
Insert Table 2.17 above figure 2.6
Table 2.15

26. Solution Example 2.13
First, we list the leading digits, called the stems, of the numbers in the table (3, 4, , 9) in a column, as shown to the left of the vertical rule. Next, we write the final digit, called the leaves, of each number from the table to the right of the vertical rule in the row containing the appropriate leading digit.
Change to page 68
Insert Table 2.17 above figure 2.6
Table 2.15
Figure 2.5

27. a. one line per stem. b. two lines per stem.
Example 2.14
A pediatrician tested the cholesterol levels of several young patients and was alarmed to find that many had levels higher than 200 mg per 100 mL. Table 2.16 presents the readings of 20 patients with high levels. Construct a stem-and-leaf diagram for these data by using
a. one line per stem. b. two lines per stem.
Change to page 69
Insert Table 2.18 above figure 2.7
Table 2.16

28. Solution Example 2.14
The stem-and-leaf diagram in Fig. 2.6(a) is only moderately helpful because there are so few stems. Figure 2.6(b) is a better stem-and-leaf diagram for these data. It uses two
lines for each stem, with the first line for the leaf digits 0-4 and the second line for the leaf digits 5-9
Change to page 69
Insert Table 2.18 above figure 2.7
Figure 2.6

29. Other Types of Graphs
A pie graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.
Pie graphs are used to show the relationship between the parts and the whole.

30. Example 2.15
Political Party Affiliations: The table shows the frequency and relative-frequency distributions for the political party affiliations of Professor Weiss’s introductory statistics students. Display the relative-frequency distribution of these qualitative data with a
a. pie chart.
b. bar graph.
Table 2.17
Change to page 62

31. Solution Example 2.15
Change to page 62
Figure 2.7

32. Reason We Travel
Reasons we travel – The following data are based on a survey from American Travel Survey on why people travel. Construct a pie graph for the data and analyze the results.
Purpose
Number
Personal Business
146
Visit Friends and Relatives
330
Work Related
225
Leisure
299

33. Reason We Travel f Percent Degree Personal Business 146 14.6% 52.56º
Visit Friends and Relatives
330
33.0%
118.8º
Work Related
225
22.5%
81.0º
Leisure
299
29.9%
107.64º
1000
100%
360º
Degree =
Percent =

34. Reason We Travel Pie Graph
Use a protractor and a compass to draw the graph
with the appropriate degree measures.
About 1/3 of the
travelers visit friends or relatives, with the fewest traveling
for personal business.
Pie Graph

35. Bar Chart
The bar chart is like a histogram, the difference is we position the bars in the bar graph so that they do not touch