Chapter 2
9
1
Chapter 2
Data Presentation Using
Descriptive Graphs
CHAPTER OVERVIEW AND OBJECTIVES
Graphical presentation has always been one of the best ways to transmit statistical information.
A
statistical graph allows you to summarize and describe a set of values from a sample or population.
Because
of the ease with which many personal computers can create and print graphs, this usage is growing.
At the
completion of this chapter, the student should be able to answer the following questions:
1.
What is a frequency distribution, and how would you construct a frequency distribution from
a set of data?
2.
How does one construct (and when is it appropriate to use) each of the following graphs:
a.
Histogram
b.
Frequency polygon
c.
Ogive
d.
Bar chart
e.
Pie chart
f.
Stemandleaf diagram
3.
What are some of the ways in which a seemingly accurate graph can be drawn in a
misleading and deceptive manner?
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10 Instructor's Manual
NOTE TO INSTRUCTORS:
Instructors, who use MINITAB, should be aware that MINITAB uses a procedure different from the
textbook in calculating quartiles.
According to the definition in the textbook, each of the quartiles of a set
of data will always be a data point or midway between two data points.
MINITAB, however, uses
interpolation.
The following procedure is used in MINITAB to find Q1 and Q3:
Q1 and Q3 are at the (N +
1)/4 and 3(N + 1)/4 positions, respectively, of the ordered data set.
If these positions are not integers,
interpolation is used.
For example, for N = 10, Q1 is at the (10 + 1)/4 = 2.75 position.
Thus, using the
second and third ordered observations (call them X
2
and X
3
), Q1 = X
2
+ .75 (X
3
 X
2
).
For Q3, 3(10 + 1)/4 =
8.25.
Hence, using the eighth and ninth ordered observations (X
8
and X
9
), Q3 = X
8
+ .25 (X
9
 X
8
).
Chapter 2 Glossary
bar chart
.
A statistical graph consisting of noncontiguous boxes useful for summarizing nominal or ordinal
data.
class
.
A data grouping in a frequency distribution, such as "10 and under 15".
class frequency
.
The number of data values contained within a
particular class.
For example, if 27 data
values are between 10 and 15 (not including 15), the class frequency for this class is 27.
class limits
.
The endpoints of each class.
For example, for the class "10 and under 15," the value 10 is the
lower class limit and 15 is the upper class limit.
class midpoint
.
The center of each class.
For example, 12.5 is the class midpoint for the class "10 and
under 15."
class width
.
The distance between adjacent lower class limits.
cumulative frequency
.
The sum of the class frequencies for a particular class and all preceding classes.
It
represents the number of data values that are less than the upper class limit of the class.
frequency distribution
.
A data summary consisting of classes, frequencies and/or relative frequencies.
frequency polygon
.
A graphical representation of a frequency
distribution consisting of dots at the top
center of each histogram box along with connecting lines.
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 Fall '11
 Pavur
 Frequency, Frequency distribution, Bar chart, Histogram

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