Business Statistics I Dr. Changping Wang
2. Frequency Distribution
lass Frequency, f
• A table that shows classes or intervals of data with a count of the
number of entries in each class.
• The frequency, f, is the number of data entries in the class.
For example,
Class Frequency, f
1 and under 5 5
5 and under 10 8
10 and under 15 6
15 under and 20 8
20 and under 25 5
25 and under 30 4
Lower boundaries: 0, 5, 10, …, 25
Upper boundaries: 5,10,15,…,30
Class width: 5
Some guidelines for the following selection.
Number of classes: 5~10 classes;
Notation for indicating classes: In this text, “and under” is used.
You may choose to use “to”, say, 0 to 5. You may use “05” or “0~5”.
Class width (CW): CW=Upper boundaryLower boundary;
Unless one has a special reason for doing so, o/w, it is best that the class
width be an “easy” number to work with. Recommended class widths are
1, 2, 2.5 (if the data has at least one decimal)
5, 10, 20, 25, 50, 100, 200, 250, etc.
0.1, 0.2, 0.25 (if the data has at least 2 decimals)
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For narrower classes For wider
classes
Dividing by 10 Multiplying by 10
0.01 0.1 1 10 100
0.02 0.2 2 20 200
0.025 0.25 2.5 25 250
0.05 0.5 5 50 500
Note: In this course, when you are asked to construct a
frequency distribution, all classes must have the same
class width.
Boundaries:
1) They should look like the data; i.e., have the same number of
decimal places as the original data.
2) Each boundary should be a multiple of the class width.
3) There must be no gaps between classes; i.e., the upper boundary
of one class =the lower boundary of the next class.
4) The minimum value must belong to the first class, and the
maximum must be in the last class.
How to determine the class width?
Estimated CW=(HL)/5
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You should choose a recommended CW (from the list of “easy” numbers)
closest to the estimated class width. When you set up CW=something,
you must check if the number of classes is between 5 and 10.
Example 1. If H=62.274 and L=119.764, then which could be the first
class of the frequency distribution?
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Example 2. The following data was about the rates (¢/min) of calling the
world from cell in Canada offered by the Startec Global Communications
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Australia 2.9¢ El Salvador 13.9¢ Jordan 10.9¢ Serbia 9.9¢
Austria 3.9¢ France 2.9¢ Korea .S 5.0¢ Spain 2.9¢
Bangladesh 3.9¢ Germany 2.9¢ Lebanon 7.9¢ Sweden 3.9¢
Bosnia 10.0¢ Greece 2.9¢ Mexico 1.9¢ Switzerland 3.9¢
Brazil 2.9¢ Guatemala 10.9¢ Pakistan 13.9¢ Syria 33.9¢
Canada 2.9¢ Ireland 2.9¢ Philippines 8.9¢ Taiwan 4.8¢
China 4.8¢ Hong Kong 3.8¢ Poland 2.9¢ Thailand 9.9¢
Colombia 1.5¢ India 1.9¢ Portugal 2.9¢ UK 2.9¢
Croatia 2.5¢ Italy 2.9¢ Russia 1.5¢ Ukraine 9.9¢
Egypt 10.0¢ Japan 5.9¢ Moscow 1.5¢ Vietnam 3¢
Construct a frequency distribution for the above data.
Example 3. The following stemandleaf plot shows the number of minutes of a
sample of Internet subscribers spent on the Internet during their most recent session.
Construct a frequency distribution following the rule in the text.
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Stem Leaf
(tens)
1 1 7 7 8 9
2 0 1 2 3 8 9 9
3 0 0 1 1 3 4 6 7 9 9 9
4 0 1 1 2 4 4 6
5 0 1 3 4 4 6 6 6 9
6 2 7 9
Example 4. Consider the following frequency distributions of the test
scores for two different sections.
Score # of students in Sec #1 # of students in Sec #2
40 and under 50 14 5
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