Graphical Displays of Data
Section 2.2
Objectives
• Create and interpret the basic types of graphs
used to display data
Introduction
• A graph is a snapshot that allows us to view
patterns at a glance without undergoing
lengthy analysis of the data.
• Graphs are much more visually appealing than
a table or list.
• A graph should be able to stand alone,
without the original data. Graph must be
given a title, as well as labels for both axes.
Purpose of Statistical Graphs
• To convey the data to the viewers in pictorial form
– It is easier for most people to comprehend the meaning of
data presented as a picture than data presented as a table.
This is especially true if the viewers have little or no
statistical knowledge
•
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•
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To describe the data set
To analyze the data set (Distribution of data set)
To summarize a data set
To discover a trend or pattern in a situation over a
period of time
• To get the viewers’ attention in a publication or
speaking presentation
Graphs Used to Display Qualitative
Data
Pie Chart
• Pie Chart is a circle that
is divided into sections
or wedges according to
the percentage of
frequencies in each
category of the
distribution.
• Show relationship of
the parts to the whole
Pareto Chart*
• Bar graph
• Used to represent a
frequency distribution
for a categorical
variable (nominal level)
and the frequencies are
displayed by the heights
of the contiguous
vertical bars, which are
arranged in order from
highest to lowest.
How do I create a Pareto Chart from a
categorical frequency distribution?
• STEP 1: Draw the x- and y-axes
• STEP 2: Label the x-axis using the qualitative
categories (highest frequency to lowest
frequency)
• STEP 3: Label the y-axis using an appropriate
scale that encompasses the high and low
frequencies
• STEP 4: Draw the contiguous vertical bars
Example
Nursing
Business Admin
Education
Computer Info Systems
Political Science
Art
General Studies
Nursing
Education
Education
Psychology
Business Admin
Psychology
Business Admin
General Studies
General Studies
General Studies
History
History
History
General Studies
Education
Computer Info Systems
Nursing
Education
General Studies
Education
History
Class (Major)
Frequency
Percentage
Art
1
3.6%
Business
Administration
3
10.7%
Computer Info
Systems
2
7.1%
Education
6
21.4%
General Studies
6
21.4%
History
4
14.3%
Nursing
3
10.7%
Political Science
1
3.6%
Psychology
2
7.1%
TOTAL
28
100%
Other Bar Graphs
Side-by-Side Bar Graph
• Used to compare different
groups
• Typically, uses different
colored bars to distinguish
groups
Stacked Bar Graph
Histogram*
• A bar graph that
displays the data from a
frequency distribution
– Horizontal Scale (x-axis)
is labeled using CLASS
BOUNDARIES or
MIDPOINTS
– Vertical Scale (y-axis) is
labeled using frequency
– NOTE: bars are
contiguous (No gaps)
How do I create a histogram from a
grouped frequency distribution?
• MINITAB
– Enter raw data into MINITAB
Example-Construct a histogram of the ages of Nextel Cup Drivers.
Use the class boundaries as the scale on the x-axis
Ages of NASCAR Nextel Cup Drivers in Years (NASCAR.com) (Data is
ranked---Collected Spring 2008)
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Frequency Polygon
• Line graph (rather than
a bar graph)
• Uses class midpoints
rather than class
boundaries on x-axis
Ogive (Cumulative Frequency Polygon)
• Line graph (rather than a
bar graph)
• Uses class boundaries on
x-axis
• Uses cumulative
frequencies (total as you
go) rather than individual
class frequencies
• Used to visually represent
how many values are
below a specified upper
class boundary
Another possibility
• We can use the
percentage (relative
frequency) rather than
the “tallies” (frequency)
on the x-axis.
– Relative Frequency
Histogram
– Relative Frequency
Polygon
– Relative Frequency
Ogive
• Used when a
comparison between
two data sets is desired,
especially if the data
sets are two different
sizes
• Overall shape
(distribution) of graph is
the same, but we use a
% on the y-axis scale
Stem and Leaf Plot*
– Method for organizing
data
– Combination of sorting
and graphing
– Original Data is retained
unlike with a grouped
frequency distribution
– “Leaves” are usually the
last digit in each data
value; right hand
column of two-column
table
– “Stems” are remaining
digits ; left hand column
of two-column table
Dotplot*(not in text)
– Graph in which each
data value is plotted as a
point (or dot) along a
single horizontal scale of
values.
– Dots representing equal
values are stacked
– Original data is retained
Exam #1 Scores in Mrs. Ralston’s
Math 1111 classes in Fall 2008
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• Construct a frequency distribution for the
Exam #1 scores. Use 8 classes with a class
width of 10 beginning with a lower class limit
of 30.
• Use the raw data to construct a histogram of
the Exam #1 scores in MINITAB
• Use the raw data to construct a dotplot of the
Exam #1 scores in MINITAB
Homework
• Page 71 #2 and 3 (create a Pareto Chart)
• Page 74 #16 (create a Stem and Leaf Plot)
• Worksheet