Presenting Data in Tables and Charts

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 2-1
Chapter 2
Presenting Data in Tables and Charts
Statistics for Managers
Using Microsoft®
Excel
4th
Edition

Chapter Goals
After completing this chapter, you should be able to:
 Create an ordered array and a stem-and-leaf display
 Construct and interpret a frequency distribution, polygon,
and ogive
 Construct a histogram
 Create and interpret bar charts, pie charts, and scatter
diagrams
 Present and interpret category data in bar charts and pie
charts
 Describe appropriate and inappropriate ways to display
data graphically

Organizing and Presenting
Data Graphically
 Data in raw form are usually not easy to use
for decision making
 Some type of organization is needed

Table

Graph
 Techniques reviewed here:
 Ordered Array
 Stem-and-Leaf Display
 Frequency Distributions and Histograms
 Bar charts and pie charts
 Contingency tables

Tables and Charts for
Numerical Data
Numerical Data
Ordered Array
Stem-and-Leaf
Display Histogram Polygon Ogive
Frequency Distributions
and
Cumulative Distributions

The Ordered Array
A sorted list of data:
 Shows range (min to max)
 Provides some signals about variability
within the range
 May help identify outliers (unusual observations)
 If the data set is large, the ordered array is
less useful

 Data in raw form (as collected):
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
 Data in ordered array from smallest to largest:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
(continued)
The Ordered Array

Stem-and-Leaf Diagram
 A simple way to see distribution details in a
data set
METHOD: Separate the sorted data series
into leading digits (the stem) and
the trailing digits (the leaves)

Example
 Here, use the 10’s digit for the stem unit:
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
 21 is shown as
 38 is shown as
Stem Leaf
2 1
3 8

Example
 Completed stem-and-leaf diagram:
Stem Leaves
2 1 4 4 6 7 7
3 0 2 8
4 1
(continued)
21, 24, 24, 26, 27, 27, 30, 32, 38, 41

Using other stem units
 Using the 100’s digit as the stem:
 Round off the 10’s digit to form the leaves

613 would become 6 1

776 would become 7 8

. . .

1224 becomes 12 2
Stem Leaf

Using other stem units
 Using the 100’s digit as the stem:
 The completed stem-and-leaf display:
Stem Leaves
(continued)
6 1 3 6
7 2 2 5 8
8 3 4 6 6 9 9
9 1 3 3 6 8
10 3 5 6
11 4 7
12 2
Data:
613, 632, 658, 717,
722, 750, 776, 827,
841, 859, 863, 891,
894, 906, 928, 933,
955, 982, 1034,
1047,1056, 1140,
1169, 1224

What is a Frequency Distribution?
 A frequency distribution is a list or a table …
 containing class groupings (categories or
ranges within which the data falls) ...
 and the corresponding frequencies with which
data falls within each grouping or category
Tabulating Numerical Data:
Frequency Distributions

Why Use Frequency Distributions?
 A frequency distribution is a way to
summarize data
 The distribution condenses the raw data
into a more useful form...
 and allows for a quick visual interpretation
of the data

Class Intervals
and Class Boundaries
 Each class grouping has the same width
 Determine the width of each interval by
 Use at least 5 but no more than 15 groupings
 Class boundaries never overlap
 Round up the interval width to get desirable
endpoints
groupingsclassdesiredofnumber
range
ervalintofWidth ≅

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

 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): 10, 20, 30, 40, 50, 60
 Compute class midpoints: 15, 25, 35, 45, 55
 Count observations & assign to classes
(continued)

Class Frequency
10 but less than 20 3 .15 15
20 but less than 30 6 .30 30
30 but less than 40 5 .25 25
40 but less than 50 4 .20 20
50 but less than 60 2 .10 10
Relative
Frequency Percentage
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
(continued)

Graphing Numerical Data:
The Histogram
 A graph of the data in a frequency distribution
is called a histogram
 The class boundaries (or class midpoints)
are shown on the horizontal axis
 the vertical axis is either frequency, relative
frequency, or percentage
 Bars of the appropriate heights are used to
represent the number of observations within
each class

Histogram: Daily High Temperature
0
3
6
5
4
2
0
0
1
2
3
4
5
6
7
5 15 25 35 45 55 More
Frequency
Class Midpoints
Histogram Example
(No gaps
between
bars)
Class
10 but less than 20 15 3
Frequency
Class
Midpoint

Histograms in Excel
Select
Tools/Data Analysis
1

Choose Histogram
2
3
Input data range and bin
range (bin range is a cell
range containing the upper class
boundaries for each class
grouping)
Select Chart Output
and click “OK”
Histograms in Excel
(continued)
(

Questions for Grouping Data
into Classes
 1. How wide should each interval be?
(How many classes should be used?)
 2. How should the endpoints of the
intervals be determined?

Often answered by trial and error, subject to
user judgment

The goal is to create a distribution that is
neither too "jagged" nor too "blocky”

Goal is to appropriately show the pattern of
variation in the data

How Many Class Intervals?
 Many (Narrow class intervals)

may yield a very jagged distribution
with gaps from empty classes

Can give a poor indication of how
frequency varies across classes
 Few (Wide class intervals)

may compress variation too much and
yield a blocky distribution

can obscure important patterns of
variation. 0
2
4
6
8
10
12
0 30 60 More
Temperature
Frequency
0
0.5
1
1.5
2
2.5
3
3.5
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
More
Temperature
Frequency
(X axis labels are upper class endpoints)

Frequency Polygon: Daily High Temperature
0
1
2
3
4
5
6
7
5 15 25 35 45 55 More
Frequency
Graphing Numerical Data:
The Frequency Polygon
Class Midpoints
Class
Frequency
Class
Midpoint
(In a percentage
polygon the vertical axis
would be defined to
show the percentage of
observations per class)

Tabulating Numerical Data:
Cumulative Frequency
Class
10 but less than 20 3 15 3 15
20 but less than 30 6 30 9 45
30 but less than 40 5 25 14 70
40 but less than 50 4 20 18 90
50 but less than 60 2 10 20 100
Total 20 100
Percentage
Cumulative
Percentage
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Frequency
Cumulative
Frequency

Graphing Cumulative Frequencies:
The Ogive (Cumulative % Polygon)
Ogive: Daily High Temperature
0
20
40
60
80
100
10 20 30 40 50 60
CumulativePercentage
Class Boundaries (Not Midpoints)
Class
Less than 10 10 0
Cumulative
Percentage
Lower
class
boundary

 Scatter Diagrams are used for
bivariate numerical data
 Bivariate data consists of paired
observations taken from two numerical
variables
 The Scatter Diagram:
 one variable is measured on the vertical
axis and the other variable is measured
on the horizontal axis
Scatter Diagrams

Scatter Diagram Example
Cost per Dayvs. Production Volume
0
50
100
150
200
250
0 10 20 30 40 50 60 70
Volume per Day
CostperDayVolume
per day
Cost per
day
23 125
26 140
29 146
33 160
38 167
42 170
50 188
55 195
60 200

Scatter Diagrams in Excel
Select the chart wizard
1
2
Select XY(Scatter) option,
then click “Next”
When prompted, enter the
data range, desired
legend, and desired
destination to complete
the scatter diagram
3

Tables and Charts for
Categorical Data
Categorical
Data
Graphing Data
Pie
Charts
Pareto
Diagram
Bar
Charts
Tabulating Data
Summary
Table

The Summary Table
Example: Current Investment Portfolio
Investment Amount Percentage
Type (in thousands $) (%)
Stocks 46.5 42.27
Bonds 32.0 29.09
CD 15.5 14.09
Savings 16.0 14.55
Total 110.0 100.0
(Variables are
Categorical)
Summarize data by category

Bar and Pie Charts
 Bar charts and Pie charts are often used
for qualitative (category) data
 Height of bar or size of pie slice shows
the frequency or percentage for each
category

Bar Chart Example
Investor's Portfolio
0 10 20 30 40 50
Stocks
Bonds
CD
Savings
Amount in $1000's
Stocks 46.5 42.27
Bonds 32.0 29.09
CD 15.5 14.09
Savings 16.0 14.55
Total 110.0 100.0
Current Investment Portfolio

Pie Chart Example
Percentages
are rounded to
the nearest
percent
Savings
15%
CD
14%
Bonds
29%
Stocks
42%
Stocks 46.5 42.27
Bonds 32.0 29.09
CD 15.5 14.09
Savings 16.0 14.55
Total 110.0 100.0

Pareto Diagram
 Used to portray categorical data
 A bar chart, where categories are shown in
descending order of frequency
 A cumulative polygon is often shown in the
same graph
 Used to separate the “vital few” from the “trivial
many”

Pareto Diagram Example
cumulative%invested
(linegraph)
%investedineachcategory(bar
graph)
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
Stocks Bonds Savings CD
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%

Tabulating and Graphing
Multivariate Categorical Data
 Contingency Table for Investment Choices ($1000’s)
Investment Investor A Investor B Investor C Total
Category
Stocks 46.5 55 27.5 129
Bonds 32.0 44 19.0 95
CD 15.5 20 13.5 49
Savings 16.0 28 7.0 51
Total 110.0 147 67.0 324
(Individual values could also be expressed as percentages of the overall total,
percentages of the row totals, or percentages of the column totals)

 Side by side bar charts
(continued)
Tabulating and Graphing
Multivariate Categorical Data
Comparing Investors
0 10 20 30 40 50 60
S tocks
B onds
CD
S avings
Investor A Investor B Investor C

Side-by-Side Chart Example
 Sales by quarter for three sales territories:
0
10
20
30
40
50
60
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
East
West
North
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
East 20.4 27.4 59 20.4
West 30.6 38.6 34.6 31.6
North 45.9 46.9 45 43.9

Principles of Graphical Excellence
 Present data in a way that provides substance,
statistics and design
 Communicate complex ideas with clarity,
precision and efficiency
 Give the largest number of ideas in the most
efficient manner
 Excellence almost always involves several
dimensions
 Tell the truth about the data

 Using “chart junk”
 Failing to provide a relative
basis in comparing data
between groups
 Compressing or distorting the vertical axis
 Providing no zero point on the vertical axis
Errors in Presenting Data

Chart Junk
Good Presentation
1960: $1.00
1970: $1.60
1980: $3.10
1990: $3.80
Minimum Wage Minimum Wage
0
2
4
1960 1970 1980 1990
$
Bad Presentation 

No Relative Basis
Good Presentation
A’s received by
students.
A’s received by
students.
Bad Presentation
0
200
300
FR SO JR SR
Freq.
10%
30%
FR SO JR SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior

listen
100
20%
0%
%

Compressing Vertical Axis
Good Presentation
Quarterly Sales Quarterly Sales
Bad Presentation
0
25
50
Q1 Q2 Q3 Q4
$
0
100
200
Q1 Q2 Q3 Q4
$


No Zero Point On Vertical Axis
Monthly Sales
0
39
42
45
J F M A M J
$
36
0
20
40
60
J F M A M J
$
Good Presentations
Monthly Sales
Bad Presentation
36
39
42
45
J F M A M J
$
Graphing the first six months of sales
or

Chapter Summary
 Data in raw form are usually not easy to use for
decision making -- Some type of organization is
needed:
♦ Table ♦ Graph
 Techniques reviewed in this chapter:
 Ordered array and stem-and-leaf display
 Frequency distributions and histograms
 Percentage polygons and ogives
 Scatter diagrams for bivariate data
 Bar charts, pie charts, and Pareto diagrams
 Contingency tables and side-by-side bar charts

Presenting Data in Tables and Charts

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