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Chapter 2 Outline
Introduction
This chapter begins our study of
descriptive statistics
.
Recall from Chapter 1 that when using
descriptive statistics we merely describe a set of data.
For example, we want to describe the
entrylevel salary for a select group of professions.
We find that the entrylevel salary for
accountants is $38,000, for systems analysts $48,000, for physician’s assistants $80,000, and so
on. This unorganized data provides little insight into the pattern of entrylevel salaries, which
makes conclusions difficult.
This chapter presents a technique that is used to organize raw data into some meaningful form.
It
is called a
frequency distribution
.
To better understand the main features of the data, we portray
the frequency distribution in the form of a frequency polygon, a histogram, or a cumulative
frequency distribution. The goal is to make tables, charts, and graphs that will quickly reveal the
shape of the data.
Constructing a Frequency Distribution
A
frequency distribution
is a useful statistical tool for organizing a mass of data into some
meaningful form.
Frequency Distribution
: A grouping of data into mutually exclusive classes
showing the number of observations in each.
As noted, a frequency distribution is used to summarize and organize large amounts of data.
The steps to follow in developing a frequency distribution are:
1.
Decide on the number of classes.
2.
Determine the class interval or width.
3.
Set the individual class limits.
4.
Tally the observations into the appropriate classes.
5.
Count the number of items in each class.
As an example, the lengths of service, in years, of a sample
of seventeen employees are given above.
The seventeen observations are
referred to as
raw data
or
ungrouped data.
To organize the
lengths of service into a frequency
distribution:
1.
We decide to have five
classes.
2.
We used a class width
of 2.
3.
We used classes 1 up to 3, 3 up to 5, and so on.
Length of Service (in
years)
4
32
10
6
6
3
2
10
6
6
5
8
4
8
4
6
2
3
3
7
5
Frequency Distribution
Lengths of
service
Tallies
Number of
employees
1 up to 3 years
//
2
3 up to 5 years
//////
6
5 up to 7 years
/////
5
7 up to 9 years
///
3
9 up to 11 yrs.
/
1
Total
17
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Tally
the lengths of service into the appropriate classes.
5.
Count the number of tallies in each class as shown.
How many classes should there be? A common guideline is from 5 to 15. Having too few or too
many classes gives little insight into the data. A rule for determining the number of classes is
shown on the next page. The size of the class interval may be a value such as 3, 5, 10, 15, 20, 50,
100, 1,000, and so on.
Class Interval
: The size or width of the class
.
The class interval can be approximated by the formula:
Class Interval
highest value lowest value
Class Interval( )
or
number of classes
H
L
i
i
k


Where:
i
is the class interval.
H
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 Spring '08
 Kassis
 Macroeconomics

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