Chapter 1
1-1
Student Lecture Notes
Organizing and Presenting
Data Graphically
Descriptive Statistics – Presenting Data with
Graphs and Tables, Learning Objectives
In this chapter you learn:
Data in raw form are usually not easy to use for
decision making
To develop tables and charts for categorical
data
Some type of organization is needed
Techniques reviewed here:
To develop tables and charts for numerical
data
The principles of properly presenting graphs
Table
Graph
Bar charts and pie charts
Pareto diagram
Ordered array
Stem-and-leaf display
Frequency distributions, histograms and polygons
Cumulative distributions and ogives
Contingency tables
Scatter diagrams
Chap 2-1
Chap 2-2
Descriptive Statistics – Graphs and Tables
Organizing Numerical Data
Organizing Numerical Data
Tabulating and Graphing Univariate Numerical Data
The Ordered Array and Stem-Leaf Display
Frequency Distributions: Tables, Histograms, Polygons
Cumulative Distributions: Tables, the Ogive
Graphing Bivariate Numerical Data
Tabulating and Graphing Univariate Categorical Data
The Summary Table
Bar and Pie Charts, the Pareto Diagram
Numerical Data
Ordered
Array
21, 24, 24, 26, 27,
Tabulating and Graphing Bivariate Categorical Data
Contingency Tables
Side by Side Bar Charts
27, 30, 32, 38, 41
Frequency Distributions
and
Cumulative Distributions
Stem and Leaf
Display
2 144677
3 028
Histograms
4 1
Graphical Excellence and Common Errors in Presenting Data
Tables
Chap 2-3
Statistics for Managers Using Microsoft Excel, 2/e
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Ogive
Polygons
Chap 2-4
© 1999 Prentice-Hall, Inc.
Chapter 1
1-2
Student Lecture Notes
Using other stem units
Organizing Numerical Data
(continued)
Data in Raw Form (as Collected):
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Data in Ordered Array from Smallest to Largest:
Largest
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
A sequence of data in rank order:
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
2
Stem-and-Leaf Display:
Separate the sorted data series into leading digits
(the stem) and the trailing digits (the leaves)
Using the 100’s digit as the stem:
The completed stem-and-leaf display:
Round off the 10’s digit to form the leaves: 613 becomes stem 6 and leaves 1
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
144677
3
028
4
1
(continued)
Stem
6
Leaves
136
7
2258
8
346699
9
13368
10
356
11
47
12
2
Chap 2-5
Chap 2-6
Tabulating and Graphing
Numerical Data
Numerical Data
Ordere
d Array
Stem and Leaf
Display
Tabulating Numerical Data:
Frequency Distributions
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Frequency Distributions
and
Cumulative Distributions
What is a Frequency Distribution?
A frequency distribution is a list or a table …
containing class groupings (ranges within which the data fall) ...
and the corresponding frequencies with which data fall within each
grouping or category
Why Use a Frequency Distribution?
Ogive
120
100
80
21, 24, 24, 26,
27, 27, 30, 32,
38, 41
60
2 144677
40
It is a way to summarize numerical data
It condenses the raw data into a more useful form...
It allows for a quick visual interpretation of the data
20
0
10
3 028
4 1
Histograms
20
30
40
50
60
Ogive
7
6
5
Tables
4
Polygons
3
2
1
0
10
20
30
40
50
60
Chap 2-7
Statistics for Managers Using Microsoft Excel, 2/e
Chap 2-8
© 1999 Prentice-Hall, Inc.
Chapter 1
1-3
Student Lecture Notes
Tabulating Numerical Data:
Frequency Distributions
Class Intervals
and Class Boundaries
Example: A manufacturer of insulation randomly selects 20
winter days and records the daily high temperature
Each class grouping has the same width
Determine the width of each interval by
Width of interval ≅
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
range
number of desired class groupings
Usually at least 5 but no more than 15
groupings
Class boundaries never overlap
Round up the interval width to get desirable
endpoints
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:
Count Observations & Assign to Classes
15, 25, 35, 45, 55
Chap 2-9
Chap 2-10
Graphing Numerical Data: The
Histogram
Frequency Distributions, Relative Frequency
Distributions and Percentage Distributions
in Excel:
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
Freq
Relative
Freq
Relative Freq
(%)
Cumulative
Freq
Cumulative
Relative
Freq
Cumulative
Relative
Freq (%)
10
but under
20
3
0.15
15%
3
0.15
15%
20
but under
30
6
0.3
30%
9
0.45
45%
30
but under
40
5
0.25
25%
14
0.7
70%
40
but under
50
4
0.2
20%
18
0.9
90%
50
but under
60
2
0.1
10%
20
1
100%
20
100%
Tools/Data Analysis/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
Chap 2-11
Statistics for Managers Using Microsoft Excel, 2/e
Chap 2-12
© 1999 Prentice-Hall, Inc.
Chapter 1
1-4
Student Lecture Notes
Graphing Numerical Data:
The Frequency Polygon
Histogram Example
Class
Midpoint Frequency
15
25
35
45
55
(No gaps
between
bars)
3
6
5
4
2
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
His togram : Daily High Te m pe rature
7
6
3
2
1
5
15
25 35 45
Class Midpoints
55
Frequency Polygon: Daily High Temperature
7
6
65
(In a percentage
polygon the vertical
axis would be defined
to show the percentage
of observations per
class)
5
4
3
2
1
0
5
15
25
35
45
55
The Ogive (Cumulative % Polygon)
65
Class Midpoints
Chap 2-13
Graphing Cumulative Frequencies:
Chap 2-14
Tables and Charts for
Univariate Categorical Data
Categorical
Data
Ogive: Daily High Temperature
100
C um u lative Percen tag e
Less than 10
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
3
6
5
4
2
4
Class Boundaries
Lower
Cumulative
class
boundar Percentage
y
0
0
10
15
20
45
30
70
40
90
50
100
15
25
35
45
55
5
0
Class
Class
Midpoint Frequency
Class
Frequency
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
Frequency
Class
Graphing Data
Tabulating Data
80
60
40
Summary
Table
20
Bar
Charts
Pie
Charts
Pareto
Diagram
0
10 10 20 20 30 30 40 40 50 50 60 60
Class Boundaries (Not Midpoints)
Chap 2-15
Statistics for Managers Using Microsoft Excel, 2/e
Chap 2-16
© 1999 Prentice-Hall, Inc.
Chapter 1
1-5
Student Lecture Notes
Graphing Univariate
Categorical Data
The Summary Table
Summarize data by category
Categorical Data
Example: Current Investment Portfolio
Investment
Amount
Percentage
Type
(in thousands $)
(%)
(Variables are
Categorical)
Stocks
Bonds
CD
Savings
46.5
32.0
15.5
16.0
Graphing Data
Tabulating Data
The Summary Table
42.27
29.09
14.09
14.55
Pie Charts
CD
S aving s
Bar Charts
Bo nd s
Total
110.0
100.0
Sto ck s
0
10
20
30
40
45
50
40
Pareto
Diagram
12 0
10 0
35
30
80
25
60
20
15
40
10
20
5
Chap 2-17
0
0
S toc ks
Bar Chart Example
Stocks
Bonds
CD
Savings
Total
Amount
Percentage
(in thousands $)
(%)
46.5
32.0
15.5
16.0
110.0
100.0
Chap 2-18
CD
Current Investment Portfolio
Investment
Type
42.27
29.09
14.09
14.55
S avin gs
Pie Chart Example
Current Investment Portfolio
Investment
Type
B on ds
Investor's Portfolio
Savings
CD
Amount
Percentage
(in thousands $)
(%)
Stocks
Bonds
CD
Savings
46.5
32.0
15.5
16.0
42.27
29.09
14.09
14.55
Total
110.0
100.0
Savings
15%
Stocks
42%
CD
14%
Bonds
Stocks
0
10
20
30
40
Bond
s 29%
50
Amount in $1000's
Chap 2-19
Statistics for Managers Using Microsoft Excel, 2/e
Percentages
are rounded
to the nearest
percent
Chap 2-20
© 1999 Prentice-Hall, Inc.
Chapter 1
1-6
Student Lecture Notes
Tabulating and Graphing
Multivariate Categorical Data
Pareto Diagram
Used to portray categorical data (nominal scale)
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”
Axis for
bar
chart
shows
%
invested
in each
category
45%
100%
40%
90%
80%
35%
70%
30%
60%
25%
Axis for
line graph
shows
cumulative
% invested
50%
20%
40%
15%
30%
10%
20%
5%
10%
0%
Contingency Table for Investment Choices ($1000’s)
Investment
Category
Investor B
Investor C
Total
Stocks
46.5
55
27.5
129
Bonds
CD
Savings
32.0
15.5
16.0
44
20
28
19.0
13.5
7.0
95
49
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)
0%
Stocks
Bonds
Savings
Chap 2-21
CD
Chap 2-22
Tabulating and Graphing
Multivariate Categorical Data
Side-by-Side Chart Example
(continued)
Investor A
Side-by-side bar charts
Sales by quarter for three sales territories:
East
W e st
North
C omparing Investors
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr
20.4
27.4
59
20.4
30.6
38.6
34.6
31.6
45.9
46.9
45
43.9
60
Savings
50
CD
40
Bonds
East
West
North
30
Stock s
20
0
10
Investor A
20
30
40
Investor B
50
10
60
0
Investor C
1st Qtr
2nd Qtr
Chap 2-23
Statistics for Managers Using Microsoft Excel, 2/e
3rd Qtr
4th Qtr
Chap 2-24
© 1999 Prentice-Hall, Inc.
Chapter 1
1-7
Student Lecture Notes
Time Series Plot Example
Scatter Diagram
Scatter plot and correlation online
scatter plot online and more
23
131
24
120
26
140
29
151
33
160
38
167
41
185
42
170
50
188
55
195
60
200
Scatter Diagrams are used to examine possible
relationships between two numerical variables
one variable is measured on the vertical axis and
the other variable is measured on the horizontal
axis
A Time Series Plot is used to study patterns in
the values of a variable over time
The Time Series Plot:
one variable is measured on the vertical axis
and the time period is measured on the
horizontal axis
Year
Number of
Franchises
1996
43
1997
54
120
250
1998
60
100
200
1999
73
2000
82
2001
95
2002
107
2003
99
2004
95
Cost per Day vs. Production Volume
150
100
50
0
0
10
20
30
40
Volum e pe r Day
50
60
Number of Franchises, 1996-2004
Nu mb e r o f
F ra n ch ise s
Cost per
day
Cost per Day
Volume
per day
80
60
40
20
0
1994
70
1996
2002
2004
2006
Chap 2-26
Principles of Graphical
Excellence
Misusing Graphs and Ethical Issues
Well-Designed Presentation of Data that
Provides:
Substance
Statistics
Design
Communicate Complex Ideas with Clarity,
Precision and Efficiency
Gives the Largest Number of Ideas in the Most
Efficient Manner
Almost Always Involves Several Dimensions
Telling the Truth about the Data
Chap 2-27
Statistics for Managers Using Microsoft Excel, 2/e
2000
Ye ar
Chap 2-25
Guidelines for good graphs:
Do not distort the data
Avoid unnecessary adornments (no “chart
junk”)
Use a scale for each axis on a two-dimensional
graph
The vertical axis scale should begin at zero
Properly label all axes
The graph should contain a title
Use the simplest graph for a given set of data
1998
Chap 2-28
© 1999 Prentice-Hall, Inc.
Chapter 1
1-8
Student Lecture Notes
‘Chart Junk’
Errors in Presenting Data
Using ‘Chart Junk’
Bad Presentation
No Relative Basis in Comparing Data between
Groups
Compressing the Vertical Axis
No Zero Point on the Vertical Axis
Good Presentation
Minimum Wage
Minimum Wage
1960: $1.00
4
$
1970: $1.60
2
1980: $3.10
0
1960
1990: $3.80
1970
1980
1990
Chap 2-29
Chap 2-30
No Relative Basis
Bad Presentation
Good Presentation
A’s received by
students
Freq.
300
200
30 %
100
10
0
0
FR SO
JR SR
Compressing Vertical Axis
Bad Presentation
A’s received by
students
Good Presentation
Quarterly Sales
200
$
50
$
Quarterly Sales
20
FR SO JR SR
100
25
0
0
Q1 Q2
Q3 Q4
Q1
Q2
Q3 Q4
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior
Chap 2-31
Statistics for Managers Using Microsoft Excel, 2/e
Chap 2-32
© 1999 Prentice-Hall, Inc.
Chapter 1
1-9
Student Lecture Notes
No Zero Point on Vertical Axis
Bad Presentation
45
$
Monthly Sales
45
42
39
36
42
39
Chapter Summary
Organized Numerical Data
Tabulated and Graphed Univariate Numerical Data
Good Presentation
Monthly Sales
$
36
J F M A M J
0
J F M A M J
Graphing the first six months of sales
The Ordered Array and Stem-Leaf Display
Frequency Distributions: Tables, Histograms, Polygons
Cumulative Distributions: Tables, the Ogive
Graphed Bivariate Numerical Data
Tabulated and Graphed Univariate Categorical Data
The Summary Table
Bar and Pie Charts, the Pareto Diagram
Tabulated and Graphed Bivariate Categorical Data
Contingency Tables
Side by Side Charts
Discussed Graphical Excellence and Common Errors in Presenting
Data
Chap 2-33
Chap 2-34
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:
Bar charts, pie charts, and Pareto diagrams
Ordered array and stem-and-leaf display
Frequency distributions, histograms and polygons
Cumulative distributions and ogives
Contingency tables and side-by-side bar charts
Scatter diagrams and time series plots
Chap 2-35
Statistics for Managers Using Microsoft Excel, 2/e
© 1999 Prentice-Hall, Inc.