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11th Edition
Chapter 2 Presenting Data in Tables and Charts

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc.

Chap 2-1

Learning Objectives
In this chapter you learn:
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To develop tables and charts for categorical data

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To develop tables and charts for numerical data
The principles of properly presenting graphs

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-2

Categorical Data Are Summarized By Tables & Graphs
Categorical Data

Tabulating Data

Graphing Data

Summary Table

Bar Charts

Pie Charts

Pareto Diagram

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-3

Organizing Categorical Data: Summary Table
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A summary table indicates the frequency, amount, or percentage of items in a set of categories so that you can see differences between categories.

Banking Preference?
ATM Automated or live telephone Drive-through service at branch

Percent
16% 2% 17%

In person at branch
Internet

41%
24%

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-4

Bar and Pie Charts
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Bar charts and Pie charts are often used for categorical data

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Length of bar or size of pie slice shows the frequency or percentage for each category

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-5

Organizing Categorical Data: Bar Chart
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In a bar chart, a bar shows each category, the length of which represents the amount, frequency or percentage of values falling into a category.
Banking Preference
Internet In person at branch Drive-through service at branch Automated or live telephone ATM 0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-6

Organizing Categorical Data: Pie Chart
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The pie chart is a circle broken up into slices that represent categories. The size of each slice of the pie varies according to the percentage in each category.
Banking Preference

16% 24% 2%

ATM Automated or live telephone Drive-through service at branch In person at branch Internet

17%

41%

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-7

Organizing Categorical Data: Pareto Diagram
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Used to portray categorical data (nominal scale)
A vertical bar chart, where categories are shown in descending order of frequency A cumulative polygon is shown in the same graph

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Used to separate the “vital few” from the “trivial many”

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-8

Organizing Categorical Data: Pareto Diagram
Pareto Chart For Banking Preference
100% 100%

% in each category (bar graph)

60% 40% 20% 0% In person Internet at branch Drivethrough service at branch ATM Automated or live telephone

60% 40% 20% 0%

Cumulative % (line graph)

80%

80%

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-9

Tables and Charts for Numerical Data
Numerical Data

Ordered Array

Frequency Distributions and Cumulative Distributions
Histogram Polygon Ogive

Stem-and-Leaf Display

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-10

Organizing Numerical Data: Ordered Array
?

? ?

An ordered array is a sequence of data, in rank order, from the smallest value to the largest value. Shows range (minimum value to maximum value) May help identify outliers (unusual observations) Day Students

Age of Surveyed College Students

16 19

17 19

17 20

18 20

18 21

18 22

22
18

25
18

27
19

32
19

38
20

42
21

Night Students

23

28

32

33

41

45
Chap 2-11

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Stem-and-Leaf Display
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A simple way to see how the data are distributed and where concentrations of data exist METHOD: Separate the sorted data series into leading digits (the stems) and the trailing digits (the leaves)

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-12

Organizing Numerical Data: Stem and Leaf Display
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A stem-and-leaf display organizes data into groups (called stems) so that the values within each group (the leaves) branch out to the right on each row.
Age of College Students

Age of Surveyed College Students

Day Students 16 19 22 17 19 25 17 20 27 18 20 32 18 21 38 18 22 42

Day Students
Stem
1 2 19 33 20 41 21 45 4 2 3

Night Students
Stem Leaf
1 2 3 4 8899 0138 23 15

Leaf
67788899 0012257 28

Night Students 18 23 18 28 19 32

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-13

Organizing Numerical Data: Frequency Distribution
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The frequency distribution is a summary table in which the data are arranged into numerically ordered classes.
You must give attention to selecting the appropriate number of class groupings for the table, determining a suitable width of a class grouping, and establishing the boundaries of each class grouping to avoid overlapping. The number of classes depends on the number of values in the data. With a larger number of values, typically there are more classes. In general, a frequency distribution should have at least 5 but no more than 15 classes. To determine the width of a class interval, you divide the range (Highest value–Lowest value) of the data by the number of class groupings desired.
Chap 2-14

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Organizing Numerical Data: Frequency Distribution Example

Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature
24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-15

Organizing Numerical Data: Frequency Distribution Example
? ? ? ? ?

Sort raw data in ascending order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find range: 58 - 12 = 46 Select number of classes: 5 (usually between 5 and 15) Compute class interval (width): 10 (46/5 then round up) Determine class boundaries (limits):
? ? ? ? ?

Class 1: Class 2: Class 3: Class 4: Class 5:

10 to less than 20 20 to less than 30 30 to less than 40 40 to less than 50 50 to less than 60

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Compute class midpoints: 15, 25, 35, 45, 55 Count observations & assign to classes

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-16

Organizing Numerical Data: Frequency Distribution Example
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Relative Frequency

Class

Frequency

Percentage

10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 Total
Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

3 6 5 4 2 20

.15 .30 .25 .20 .10 1.00

15 30 25 20 10 100
Chap 2-17

Tabulating Numerical Data: Cumulative Frequency
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Class 10 but less than 20 20 but less than 30

Frequency Percentage 3 6 15 30

Cumulative Cumulative Frequency Percentage 3 9 15 45

30 but less than 40
40 but less than 50 50 but less than 60

5
4 2

25
20 10

14
18 20

70
90 100

Total

20

100
Chap 2-18

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Why Use a Frequency Distribution?

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It condenses the raw data into a more useful form

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It allows for a quick visual interpretation of the data
It enables the determination of the major characteristics of the data set including where the data are concentrated / clustered
Chap 2-19

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Frequency Distributions: Some Tips
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Different class boundaries may provide different pictures for the same data (especially for smaller data sets)
Shifts in data concentration may show up when different class boundaries are chosen As the size of the data set increases, the impact of alterations in the selection of class boundaries is greatly reduced When comparing two or more groups with different sample sizes, you must use either a relative frequency or a percentage distribution
Chap 2-20

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Organizing Numerical Data: The Histogram
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A vertical bar chart of the data in a frequency distribution is called a histogram.
In a histogram there are no gaps between adjacent bars. The class boundaries (or class midpoints) are shown on the horizontal axis.

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The vertical axis is either frequency, relative frequency, or percentage.
The height of the bars represent the frequency, relative frequency, or percentage.
Chap 2-21

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Organizing Numerical Data: The Histogram
Class Frequency Relative Frequency

Percentage 15 30 25 20 10 100

10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 Total

3 6 5 4 2 20

.15 .30 .25 .20 .10 1.00

Histogram : Daily High Tem perature 7 6
Frequency

5 4 3 2 1 0 5 15 25 35 45 55 More

(In a percentage histogram the vertical axis would be defined to show the percentage of observations per class)

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-22

Organizing Numerical Data: The Polygon
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A percentage polygon is formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoints at their respective class percentages.
The cumulative percentage polygon, or ogive, displays the variable of interest along the X axis, and the cumulative percentages along the Y axis. Useful when there are two or more groups to compare.

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-23

Graphing Numerical Data: The Frequency Polygon
Class 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 Class Midpoint Frequency 15 25 35 45 55 3 6 5 4 2

Frequency Polygon: Daily High Temperature 7 6 5 4 3 2 1 0 5 15 25 35 45 55 65

(In a percentage polygon the vertical axis would be defined to show the percentage of observations per class)
Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Frequency

Class Midpoints
Chap 2-24

Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon)
Class 10 but less than 20 20 but less than 30 30 but less than 40 40 but less than 50 50 but less than 60 Lower % less class than lower boundary boundary 10 20 30 40 50 15 45 70 90 100

Ogive: Daily High Temperature
Cumulative Percentage

100 80 60 40 20 0 10 20 30 40 50 60
Lower Class Boundary

(In an ogive the percentage of the observations less than each lower class boundary are plotted versus the lower class boundaries.

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-25

Cross Tabulations
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Used to study patterns that may exist between two or more categorical variables. Cross tabulations can be presented in:
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Tabular form -- Contingency Tables Graphical form -- Side by Side Charts

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-26

Cross Tabulations: The Contingency Table
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A cross-classification (or contingency) table presents the results of two categorical variables. The joint responses are classified so that the categories of one variable are located in the rows and the categories of the other variable are located in the columns. The cell is the intersection of the row and column and the value in the cell represents the data corresponding to that specific pairing of row and column categories. A useful way to visually display the results of crossclassification data is by constructing a side-by-side bar chart.

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-27

Cross Tabulations: The Contingency Table
A survey was conducted to study the importance of brand name to consumers as compared to a few years ago. The results, classified by gender, were as follows:
Importance of Brand Name Male Female Total

More
Equal or Less Total

450
3300 3750

300
3450 3750

750
6750 7500

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-28

Cross Tabulations: Side-By-Side Bar Charts

Importance of Brand Name

Less or Equal

Response

More

Female Male

0

500

1000

1500

2000

2500

3000

3500

4000

Number of Responses

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-29

Scatter Plots
? Scatter plots are used for numerical data consisting of paired observations taken from two numerical variables
? One variable is measured on the vertical axis and the other variable is measured on the horizontal axis ? Scatter plots are used to examine possible relationships between two numerical variables

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-30

Scatter Plot Example
Volume per day 23 26 29 33 38 Cost per day 125 140 146 160 167
Cost per Day

Cost per Day vs. Production Volume
250 200 150 100 50 0 20 30 40 50 60 70 Volume per Day

42
50 55 60

170
188 195 200

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-31

Time Series Plot
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A Time Series Plot is used to study patterns in the values of a numeric variable over time
The Time Series Plot: ? Numeric variable is measured on the vertical axis and the time period is measured on the horizontal axis

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Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-32

Time Series Plot Example
Number of Franchises 43
Number of Franchises

Year 1996 1997 1998 1999 2000 2001 2002 2003 2004

Number of Franchises, 1996-2004
120 100 80 60 40 20 0 1994 1996 1998 2000 Year 2002 2004 2006

54 60 73 82 95 107 99 95

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-33

Principles of Excellent Graphs
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The graph should not distort the data. The graph should not contain unnecessary adornments (sometimes referred to as chart junk). The scale on the vertical axis should begin at zero. All axes should be properly labeled. The graph should contain a title. The simplest possible graph should be used for a given set of data.

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-34

Graphical Errors: Chart Junk
Minimum Wage
1960: \$1.00 1970: \$1.60

? Good Presentation
\$
4 2

Minimum Wage

1980: \$3.10

0
1990: \$3.80

1960

1970

1980

1990

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-35

Graphical Errors: No Relative Basis
Freq. 300 200

?Good Presentation
% 30% 20% 10% 0% FR SO JR SR

100
0 FR SO JR SR

FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior
Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc.. Chap 2-36

Graphical Errors: Compressing the Vertical Axis
Quarterly Sales
200 100

? Good Presentation
\$
50 25

Quarterly Sales

\$

0
Q1 Q2 Q3 Q4

0
Q1 Q2 Q3 Q4

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-37

Graphical Errors: No Zero Point on the Vertical Axis
\$ 45 42 39

?
45 42 39 36

Good Presentations
Monthly Sales

Monthly Sales

\$

36
J F M A M J

0

J

F

M

A

M

J

Graphing the first six months of sales

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-38

Chapter Summary
In this chapter, we have ? Organized categorical data using the summary table, bar chart, pie chart, and Pareto diagram. ? Organized numerical data using the ordered array, stem-andleaf display, frequency distribution, histogram, polygon, and ogive. ? Examined cross tabulated data using the contingency table and side-by-side bar chart. ? Developed scatter plots and time series graphs. ? Examined the do’s and don'ts of graphically displaying data.

Basic Business Statistics, 11e ? 2009 Prentice-Hall, Inc..

Chap 2-39