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Quantitative Methods

QMS 102

Changping Wang

Fall

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Business Statistics I Dr. Changping Wang
4.4. Box-Whisker Plot
For numerical data, we can use frequency histogram
and relative frequency histogram to get
understanding of the shape of the distribution. In this
section, we introduce a new concept: the box-
whisker-plot. The Box-Whisker Plot is a graphical
display that is used to get a general picture of a set
of data. The main difference from the box-whisker-
plot and previous graphical display is that the box-
whisker-plot shows some the values of descriptive
statistics. In particular, it shows five-number
summary:
Minimum, Q1, Median, Q3 and Maximum
To draw a Box-Whisker Plot, we need
a.Find the five-number summary of the data
set.
b.Construct an appropriate horizontal scale.
c. To form a box with Q1 and Q3 determining
the location of the sides.
d.The median is indicated by a line across the
box; and the mean may be indicated with a
“+” sign.
e.To draw the whiskers, we follow
a)They cannot past the inner fences;
b)They must end at a data point.
Session 7 Page 1 Business Statistics I Dr. Changping Wang
How to calculate the location for the inner and
outer fences?
LIF=Q1-1.5*IQR;
RIF=Q3+1.5*IQR;
LOF=Q1-3*IQR;
ROF=Q3+3*IQR
Note: (1) LIF=Left Inner Fence; LOF=Left Outer
Fence;
(2) RIF=Right Inner Fence; ROF=Right Outer
Fence;
(3) All data values that fall between the
fences are call suspected outliers, using “o” to
indicate them; All data values that lie beyond the
outer fences are call outliers, using “*” to indicate
them.
Session 7 Page 2 Business Statistics I Dr. Changping Wang
EXAMPLE 1: The test score of 15 employees
enrolled in a CPR training course are listed as follows:
13, 9, 18, 15, 14, 21, 7, 10, 11, 20, 5, 18, 37, 16,
17.
Draw a Box-Whisker Plot.
Session 7 Page 3 Business Statistics I Dr. Changping Wang
EXAMPLE 2: The “Gasoline and fuel oil, average retail
prices by urban centre” appeared in Statistics Canada.
Gasoline and fuel oil, average retail prices by urban
centre
(regular unleaded gasoline at self service filling
stations)
regular unleaded gasoline at self
service filling stations
Cents per litre
July July July July July
2005 2006 2007 2008 2009
St John’s 104.0 116.5 116.5 146.8 109.6
Saint John 100.3 112.8 106.8 137.2 97.1
Halifax 100.4 115.1 112.7 142.2 101.6
Quebec 101.4 115.1 113.3 142.5 102.3
Montreal 98.9 114.1 107.4 143.5 100.1
Ottawa 91.6 105.2 101.2 130.2 89.5
Toronto 90.1 105.7 101.0 132.0 93.9
Thunder 94.6 113.8 114.2 140.3 106.8
Bay
Winnipeg 92.5 110.7 112.4 135.6 99.8
Regina 92.7 112.4 113.5 136.0 102.5
Saskatoon 96.9 114.3 114.9 135.5 102.9
Edmonton 88.6 105.8 105.6 130.3 89.6
Calgary 90.2 106.0 109.0 132.2 92.5
Vancouver 99.5 116.0 109.8 146.6 108.1
Victoria 101.4 115.2 111.4 150.5 105.2
Whitehors 106.3 116.3 118.6 144.4 106.3
e
Yellowknif 103.5 119.3 127.1 150.0 119.2
e
Source: Statistics Canada, CANSIM, table (for fee) 326-0009
and Catalogue no.
62-001-X
Last Modified: 2009-08-24
For the date in 2007, draw a Box-Whisker Plot.
Session 7 Page 4 Business Statistics I Dr. Changping Wang
EXAMPLE 3: The following data was about the rates
(¢/min) of calling the world from cell in Canada offered by
the Startec Global Communications .
13.9 10.9
Australia 2.9¢ El Salvador ¢ Jordan ¢ Serbia 9.9¢
Austria 3.9¢ France 2.9¢ Korea .S 4.9¢ Spain 2.9¢
Bangladesh3.9¢ Germany 2.9¢ Lebanon 7.9¢ Sweden 3.9¢
Bosnia 9.9¢ Greece 2.9¢ Mexico 1.9¢ Switzerland 3.9¢
Brazil 2.9¢ Guatemala 10.9 Pakistan 13.9 Syria 13.9
¢ ¢ ¢
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¢
1.5
Colombia ¢ India 1.9¢ Portugal 2.9¢ UK 2.9¢
Croatia 2.5¢ Italy 2.9¢ Russia 1.5¢ Ukraine 9.9¢
Egypt 9.9¢ Japan 5.9¢ Moscow 1.5¢ Vietnam 3¢
Help a marketing analyst in the Startec Global
Communications to construct a box-whisker plot for the
above data by computing each of the following using a
CASIO calculator: (If necessary, round your answers to
one decimal place. All answers are in ¢/min)
Question 1 The first quartile is
a) 2.8 b) 2.2 c) 4.3 d) 2.9 e) None of these
Question 2 The third quartile is
a) 7.9 b) 9.4 c) 3.1 d) 9.0 e) None of these
Question 3 The interquartile range is
a) 7.9 b) 7.2 c) 9.7 d) 6.5 e) None of these
Question 4 The right inner fence is
Session 7 Page 5 Business Statistics I Dr. Changping Wang
a) 19.2 b) 16.9 c) 19.3 d)12.7 e)None of these
Question 5 The right outer fence is
a) 22.4 b) 21.4 c) 32.7 d) 28.9 e) None of these
Question 6 The smallest value on the left whisker (i.e. the
left whisker ends at what value) is
a) 2.5 b)1.9 c) - 6.9 d) -16.6 e)None of these
Question 7 The largest value on the right whisker (i.e. the
right whisker ends at what value) is
a) 13.9 b)28.9 c) 4.0 d) 10.5 e)None of
these
Question 8 In the box-whisker plot, the total number of
suspected outliers is:
a) 0 b)1 c) 2 d) 3 e)4
Question 9 In the box-whisker plot, the total number of
outliers is:
a) 0 b)1 c) 2 d) 3 e) None of these
Session 7 Page 6 Business Statistics I Dr. Changping Wang
5.1: Basic Probability Concepts
We often speak of events and their chance, or
probability of occurring. The probability and chance
are often the same word. When we do not exactly
know the outcome in advance, we speak of chance.
e.g. Chance of a team winning; chance of winning a
lottery; chance of rolling a six (die); chance of raining
tomorrow.
We can be certain of few things:
e.g. Certain that the sun will rise; certain that there
will be school in the winter.
To introduce the concept of probability, one has to
introduce sample space, events.
The general setting is: we perform an experiment (of
interest) which can have a number of outcomes. The
sample space, denoted by S, is the set of all
possible outcomes of the experiment.
e.g. If I toss a coin three times and record the result,
then S={HHH,HHT, HTH, THH, HTT,THT,TTH,TTT}
e.g. If I toss a coin three t

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