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Lecture

# QMS 102 Chapter 2

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Ryerson University

Quantitative Methods

QMS 102

Armand Gervais

Fall

Description

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
0 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 “0-5” or “0~5”.
Class width (CW): CW=Upper boundary-Lower
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)
Session 2 Page 1 Business Statistics I Dr. Changping Wang
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.
Session 2 Page 2 Business Statistics I Dr. Changping Wang
How to determine the class width?
Estimated CW=(H-L)/5
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.
Session 2 Page 3 Business Statistics I Dr. Changping Wang
Example 1. If H=-62.274 and L=-119.764, then
which could be the first class of the frequency
distribution?
Session 2 Page 4 Business Statistics I Dr. Changping Wang
Example 2. The following data was about the rates
(¢/min) of calling the world from cell in Canada offered by
the Startec Global Communications
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.
Session 2 Page 5 Business Statistics I Dr. Changping Wang
Example 3. The following stem-and-leaf 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.
Stem Leaf
(tens)
0 7 7
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
7 2 3 7 8
8 0 6
Example 4. Consider the following frequency distributions of the test
scores for two different sections.
Session 2 Page 6 Business Statistics I Dr. Changping Wang
Score # of students in Sec #1 # of students in Sec #2

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