Outline
Other Types of Graphs
Lecture 4, STAT 2246
Julien Dompierre
Département de mathématiques et d’informatique
Université Laurentienne
14 janvier 2007, Sudbury
Julien Dompierre
1
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Outline
1
Other Types of Graphs
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Julien Dompierre
2
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Outline
1
Other Types of Graphs
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Julien Dompierre
3
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Vilfredo Pareto
Vilfredo Federico Damaso Pareto (b. July
15, 1848, Paris – d. August 19, 1923,
Geneva) was an Italian sociologist, economist and philosopher.
In 1906 he made the famous observation
that twenty percent of the population owned
eighty percent of the property in Italy, later
generalised by Joseph M. Juran and others into the so-called Pareto principle (also
termed the 80-20 rule) and generalised further to the concept of a Pareto distribution.
Julien Dompierre
4
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Pareto Chart (p. 64)
If the data can be placed in specific categories, such as qualitative
or categorical variables, a Pareto chart can be used.
A Pareto chart is used to represent a frequency distribution for a
categorical variable, and the frequencies are displayed by the
heights of vertical bars, which are arranged in order from highest
to lowest.
Julien Dompierre
5
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Example of a Pareto Chart (p. 64)
The table shown here is the average cost per mile for passenger
vehicles on state turnpikes.
State
Indiana
Oklahoma
Florida
Maine
Pennsylvania
Cost
2.96 c
4.36 c
6.06 c
3.86 c
5.86 c
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Drawing a Pareto Chart
1. Arrange the data form largest to smallest according to
frequency.
2. Make the bars the same size.
3. Make the space between the bar equal.
4. Make the units that are used for the frequency equal in size.
5. Draw the bars corresponding to the frequencies.
Julien Dompierre
7
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Outline
1
Other Types of Graphs
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Julien Dompierre
8
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Time Series Graph
A time series graph represents data that occur over a specific
period of time.
Step 1: Draw and label the x and y axes.
Step 2: Label the x axis for the time and the y axis for the data.
Step 3: Plot each point according to the table.
Step 4: Draw line segments connecting adjacent points. Do not
try to fit a smooth curve through the data points.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Example (Exercise 6, p. 78)
Draw a time series graph to
represent the data for the number of airline departures (in millions) for the given years.
Year
1996
1997
1998
1999
2000
2001
2002
Number of
departures
7.9
9.9
10.5
10.9
11.0
9.8
10.1
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Compound Time Series Graph (p. 66)
Two data sets (or more) can be compared on the same graph
(called a compound time series graph) if two lines (or more) are
used.
(Exercise 20, p. 79) The number of successful space launches
by the United States and Japan
for the years 1993-1997.
Year
1993
1994
1995
1996
1997
U.S
29
27
24
32
37
Japan
1
4
2
1
2
Julien Dompierre
11
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Outline
1
Other Types of Graphs
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Julien Dompierre
12
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
The Pie Graph (p. 67)
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.
The purpose of the pie graph
is to show the relationship of
the parts to the whole by visually comparing the sizes of
the sections. Percentages or
proportions can be used. The
variable is nominal or categorical.
Julien Dompierre
13
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Steps to Construct a Pie Graph (p. 67–68)
Step 1: Since there are 360 degrees in a circle, the frequency for
each class must be converted into a proportional part of the circle.
This conversion is done by using the formula
Degrees =
f
· 360◦
n
where f = frequency for each class and n = sum of the
frequencies. The degrees should sum to 360.
Julien Dompierre
14
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Steps to Construct a Pie Graph (p. 67–68)
Step 2: Each frequency must also be converted to a percentage
using the formula
f
% = · 100%
n
Step 3: Next, using a protractor and a compass, draw the graph
using the appropriate degree measures found in step 1, and label
each section with the name and percentages.
Julien Dompierre
15
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Outline
1
Other Types of Graphs
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Julien Dompierre
16
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Misleading Graphs (p. 70)
Graphs give a visual representation that enables readers to analyze
and interpret data more easily than they could simply by looking at
numbers. However, inappropriately drawn graphs can misrepresent
the data and lead the reader to false conclusions.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Misleading Graphs (p. 70)
When the graph is redrawn using a scale that goes from 0 to
100%, there is hardly a noticeable difference in the percentages.
Thus, changing the units at the starting point on the y axis can
convey a very different visual representation of the data.
Julien Dompierre
18
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Misleading Graphs (p. 71)
Julien Dompierre
19
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Misleading Graphs (p. 72)
Julien Dompierre
20
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Misleading Graphs – Bad Scaling (p. 72)
Another misleading graphing technique sometimes used involves
exaggerating a one-dimensional increase by showing it in two
dimensions.
Julien Dompierre
21
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Misleading Graphs – Bad Labelling (p. 72)
Another way to misrepresent data on a graph is by omitting
labels or units on the axes of the graph.
Graphs and charts should always be labeled and titled.
On all graphs and charts, equal spaces should always represent
equal amounts.
Finally, all graphs should contain a source for the information
presented. The inclusion of a source for the data will enable you to
check the reliability of the organization presenting the data.
Julien Dompierre
22
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Outline
1
Other Types of Graphs
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Julien Dompierre
23
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Stem and Leaf Plots (p. 73)
A stem and leaf plot is a data plot that uses part of the data
value as the stem and part of the data value as the leaf to form
groups or classes.
The stem and leaf plot is a method of organizing data and is a
combination of sorting and graphing. It has the advantage over a
grouped frequency distribution of retaining the actual data while
showing them in graphical form.
Julien Dompierre
24
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Steps to Construct a Stem and Leaf Plot (p. 74)
Step 1: Arrange the data in order. (Note: Arranging the data in
order is not essential and can be cumbersome when the data set is
large; however, it is helpful in constructing a stem and leaf plot).
The leaves in the final stem and leaf plot should be arranged in
order.
Step 2: Separate the data according to the first digit.
Step 3: A display can be made by using the leading digit as the
stem and the trailing digit as the leaf.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Back-to-Back Stem and Leaf Plot (p. 76)
Related distributions can be compared by using a back-to-back
stem and leaf plot. The back-to-back stem and leaf plot uses the
same digits for the stems of both distributions, but the digits that
are used for the leaves are arranged in order out from the stems on
both sides.
Atlanta
| Philadelphia
-------------------------------55 70 44 36 40 | 61 40 38 32 30
63 40 44 34 38 | 58 40 40 25 30
60 47 52 32 32 | 54 40 36 30 30
50 53 32 28 31 | 53 39 36 34 33
52 32 34 32 50 | 50 38 36 39 32
26 29
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Atlanta
| Philadelphia
-------------------------------55 70 44 36 40 | 61 40 38 32 30
63 40 44 34 38 | 58 40 40 25 30
60 47 52 32 32 | 54 40 36 30 30
50 53 32 28 31 | 53 39 36 34 33
52 32 34 32 50 | 50 38 36 39 32
26 29
Atlanta
Philadelphia
------------------------------986 | 2 | 5
8644222221 | 3 | 000022346668899
74400 | 4 | 0000
532200 | 5 | 0348
30 | 6 | 1
0 | 7 |
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Outline
1
Other Types of Graphs
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Julien Dompierre
28
Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Paired Data and Scatter Plots (p. 86)
Many times researchers are interested in determining if a
relationship between two variables exists. In order to accomplish
this, the researcher collects data consisting of two measures that
are paired with each other. The first measure is called the
independent variable, designated as x, and the second variable, is
called the dependent variable, and designated as y .
Once a set of order pairs (x, y ) of data values is collected, a graph
can be drawn to represent the data. This graph is called a scatter
plot or scatter diagram.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Paired Data and Scatter Plots (p. 86)
A scatter plot is a graph of order pairs of data values that is used
to determine if a relationship exists between the two variables.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Analyzing Scatter Plot (p. 87)
A positive linear relationship exists when the points fall
approximately in an ascending straight line and both the x and y
values increase at the same time.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Analyzing Scatter Plot (p. 87)
A negative linear relationship exists when the points fall
approximately in a descending straight line from left to right.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Analyzing Scatter Plot (p. 87)
A nonlinear relationship exists when the points fall in a curved
line. The relationship is described by the nature of the curve.
Julien Dompierre
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Outline
Pareto Charts
Time Series Graphs
Pie Graphs
Misleading Graphs
Stem and Leaf Plots
Paired Data and Scatter Plots
Analyzing Scatter Plot (p. 87)
No relationship exists when there is no discernible pattern of the
points.
Julien Dompierre
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