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SCATTER DIAGRAMS AND SOME CHARTS
Content
• Scatter diagrams
• Some charts
– Pie charts
– Bar charts
– Line charts
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SCATTTER DIAGRAMS
• Often, we are interested in two variables. For
example, we may want to know the relationship
between
– advertising and sales
– experience and time required to produce an unit of
a product
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SCATTTER DIAGRAMS
• Scatter diagrams show how two variables are related
to one another
– To draw a scatter diagram, we need a set of two
variables
– Label one variable x and the other y
– Each pair of values of x and y constitute a point on
the graph
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SCATTTER DIAGRAMS
• In some cases, the value of one variable may depend
on the value of the other variable. For example,
– sales depend on advertising
– time required to produce an item of a product
depend on the number of units produced before
• In such cases, the first variable is called dependent
variable and the second variable is called
independent variable. For example,
Independent variable
Dependent variable
Advertising
Sales
Number of units produced
Production time/unit
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SCATTTER DIAGRAMS
• Usually, independent variable is plotted on the
horizontal axis (x axis) and the dependent variable on
the vertical axis (y axis)
• Sometimes, two variables show some relationships
– positive relationship: two variables move together
i.e., one variable increases (or decreases)
whenever the other increases (or, decreases).
Example: advertising and sales.
– negative relationship: one variable increases (or,
decreases) whenever the other decreases
(increases). Example: number of units produced
and production time/unit
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SCATTTER DIAGRAMS
• Relationship between two variables may be linear or
non-linear. For example,
– the relationship between advertising and sales
may be linear.
– the relationship between number of units
produced and the production time/unit may be
nonlinear.
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SCATTTER DIAGRAMS (EXAMPLE)
Advertizing
1,000 of dollars
1
3
5
4
2
5
3
2
Sales
1,000 of dollars
30
40
40
50
35
50
35
25
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SCATTER DIAGRAM
Sales
60
40
20
0
2
4
6
Advertising
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SCATTTER DIAGRAMS (EXAMPLE)
Number of units
produced
10
25
10
250
500
1000
5000
10000
Production time
hours/unit
9.22
4.85
3.8
2.44
1.7
1.03
0.6
0.5
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Production time (hours)/unit
SCATTER DIAGRAM
10
5
0
0
2000
4000
6000
8000
Number of units produced
10000
12000
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PIE CHARTS
• A pie chart is the most popular graphical method for
summarizing quantitative/nominal data
• A pie chart is a circle is subdivided into a number of
slices
• Each slice represents a category
• Angle allocated to a slice is proportional to the
proportion of times the corresponding category is
observed
• Since the entire circle corresponds to 3600, every 1%
of the observations corresponds to 0.01  3600 = 3.60
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PIE CHARTS (EXAMPLE)
Code
of Area
1
2
3
4
5
Area
Number
Proportion Angles on a
of Graduates of Graduates Pie Chart
Accounting
73
Finance
52
General Mgmnt
36
Marketing
64
Other
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PIE CHART
5 More
11% 0%
1
29%
4
25%
3
14%
2
21%
1
2
3
4
5
More
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BAR CHARTS
• Bar charts graphically represent the frequency or
relative frequency of each category as a bar rising
vertically
• The height of each bar is proportional to the
frequency or the relative frequency
• All the bars must have the same width
• A space may be left between bars
• Bar charts may be used for qualitative data or
categories that should be presented in a particular
order such as years 1995, 1996, 1997, ...
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BAR CHARTS (EXAMPLE)
Code
of Area
1
2
3
4
5
Area
Number
of Graduates
Accounting
73
Finance
52
General Mgmnt
36
Marketing
64
Other
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Count of Area
BAR CHART
80
70
60
50
40
30
20
10
0
1
2
3
4
5
Area
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LINE CHARTS
• Line charts are often used when the categories are
points in time. Such a chart is called a time-series
chart. For example, consider a graph that shows
monthly or weekly sales data.
• Frequency of each category is represented by a point
above and then points are joined by straight lines
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LINE CHARTS (EXAMPLE)
Year
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
Fatal Accidents
Number of Passengers
Per 1,000 Departures
Millions
0.10
21
0.23
27
0.24
28
0.02
29
0.31
32
0.04
36
0.12
38
0.04
42
0.24
42
0.15
48
0.10
53
18
0.04
58
Line Chart
Fatal Accidents
Per 1,000 Departures
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
6
7
8
9 10 11 12
Year
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Number of Passengers
(Millions)
Line Chart
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10 11 12
Year
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CHOICE OF A CHART
• Pie chart
– Small / intermediate number of categories
– Cannot show order of categories
– Emphasizes relative values e.g., frequencies
• Bar chart
– Small / intermediate/large number of categories
– Can present categories in a particular order, if any
– Emphasizes relative values e.g., frequencies
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CHOICE OF A CHART
• Bar chart
– Small/intermediate/large number of categories
– Can present categories in a particular order, if any
– Emphasizes relative values e.g., frequencies
• Line chart
– Small/intermediate/large number of categories
– Can present categories in a particular order, if any
– Emphasizes trend, if any
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EFFECTIVE USE OF GRAPHICAL TECHNIQUES
1. Tables may be used for small data sets and graphs
for large data sets
2. A graph must convey an idea or a concept
3. If a graph shows two or more variables, the
relationship between the variables must be clearly
described
4. A graph must emphasize fact, not color, picture or
other form of the graph
5. A graph must not distort facts
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