Section 2.1
Summer 2013 - Math 1040
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Roadmap
Our focus will be on quantitative data sets.
Be able to write frequency distributions.
Compute ranges, midpoints, relative frequencies, and
cumulative frequencies.
Contruct histograms, frequency polygons, and ogives.
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Frequency distribution
A frequency distribution is a table for the number of times entries in a
data set belong to a class. The frequency of a class is the number of
data entries in the class.
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Frequency distribution
A frequency distribution is a table for the number of times entries in a
data set belong to a class. The frequency of a class is the number of
data entries in the class.
With quantitative data classes are intervals whose width is determined by
the range and how many classes to have.
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Frequency distribution
A frequency distribution is a table for the number of times entries in a
data set belong to a class. The frequency of a class is the number of
data entries in the class.
With quantitative data classes are intervals whose width is determined by
the range and how many classes to have.
The range is the difference between the maximum and mininum data
entries.
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Guidelines
1
Choose a number for the number of classes. (5 - 20)
2
Find the class width: Find the range first, then take the number from
step 1 and divide the range by that number. Round for convenience.
3
Find the class limits. One option is to start with the minimum and
add the class width, repeating but avoiding overlaps/double counts.
4
Mark a tally for each data entry.
5
Count the tallies to find the frequency for each class.
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Data sets
The data set for the first example: Prices (in US dollars) of 30 portable
GPS navigators.
90
275
220
130
270
100
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400
150
200
200
130
400
350
59
200
70
200
250
325
160
95
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450
180
150
300
170
250
130
150
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Features of the data
Features of the data may be included with the frequency distribution.
The midpoint of a class is the sum of the upper and lower limits divided
by two. This is sometimes called the class mark.
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Features of the data
Features of the data may be included with the frequency distribution.
The midpoint of a class is the sum of the upper and lower limits divided
by two. This is sometimes called the class mark.
The relative frequency is the percentage of data entries that are in a
class.
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Features of the data
Features of the data may be included with the frequency distribution.
The midpoint of a class is the sum of the upper and lower limits divided
by two. This is sometimes called the class mark.
The relative frequency is the percentage of data entries that are in a
class.
The cumulative frequency is the sum of frequencies of the class and all
classes before.
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Formulas
Use f for frequency, n for sample size, and σ, sigma, to mean addition.
Class width
=
Range
Number of Classes
(Round.)
Midpoint
=
(Lower class limit + Upper class limit)
2
Relative frequency
=
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Class frequency
f
=
Sample size
n
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Assignments
Assignment:
1
Read pages 38-41.
2
Try exercises 1-15 odd on page 47.
Vocabulary: frequency distribution, range, classes, midpoint, relative
frequency, cumulative frequency
Understand: Construct a frequency diagram by choosing the number of
classes, finding class width from the range, writing the class limits, and
tallying frequencies.
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