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Quantitative Methods
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QMS 102
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Chapter 2

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Quantitative Methods

QMS 102

Jason Chin- Tiong Chan

Fall

Description

QMS102-Business Statistics I Chapter 2 and 3
Chapter 2 and 3 Organize Qualitative and
Quantitative Data Graphically
Today’s Outcomes
1. Review-Chapter1 and Chapter3.1
2. Create tables, bar graphs, pie charts and line graphs for qualitative
(categorical) data
3. Create frequency distributions, and graphical charts (histogram and ogive)
for quantitative (numerical) data
Variables
1. A characteristic or quantity that can vary
2. Example: Gender, age, cleanliness rating, staff friendliness rating, and
purchase amount.
Qualitative(Categorical) and Quantitative(Numerical) data
Qualitative data
1. Data containing descriptive information in words or numbers (numbers
represent codes for associated words)
2. Example: Gender, staff friendliness rating, customer satisfaction
Quantitative data
1. Data containing numerical information.
2. Example: Age, purchase amount
Quantitative Data: Discrete and Continuous data
Discrete data
1. Data that can take only certain values within a given range.
2. Example: number of customers
Continuous data
1. Data that can take on infinite possible values within a given range
2. Example: purchase amount
Example1
Part I: Classify the following sets of data as categorical or numerical
___________ a. The amount of investment in Tax-Free Savings Account (TFSA)
___________ b. The client’s gender
Fall2012 Page #1 QMS102-Business Statistics I Chapter 2 and 3
___________ c. The interest rate (in percent)
__________ d. Employee’s performance
__________ e. The number of customers in the Ryerson Bank.
Part II: Classify the following sets of data as continuous or discrete
____________ f. The number of clients who have TFSA with Ryerson Bank
____________ g. The average yearly salary for a Certified General Accountant
____________ h. The month(s) in which a firm’s employees choose to take their
vacations.
____________ i. The daily closing price of the Ryerson.COM stock.
Tables, Bar Charts and Pie Charts for Qualitative(Categorical)
Data
Tables
Consists of one variable
Cross-classification Table/ Crosstabs / Contingency Tables
Consists of two variables
Bar Charts
Bar Chart shows each category, the length of each represent the amount,
frequency or percentage of values falling into a category.
Pie Charts
1. A circle divided into sectors whose areas are proportional to the quantities
represented.
2. It shows relative comparison- in term of percentage. (It is the best way of
comparing individual categories to the total)
3. The following information has to be included in pie chart: title, legend and
count/%.
Fall2012 Page #2 QMS102-Business Statistics I Chapter 2 and 3
Example1:
The following data show the mode of transportation that 30 people used to
commute to work during the last summer. These 30 people live and work in the
GTA.
No. Gender Age Mode of No. Gender Age Mode of
Group Transportation Group Transportation
to work to work
1 Male 16-25 Bicycle 16 Female 16-25 Bicycle
2 Female 36-45 Walking 17 Female 26-35 TTC
3 Male 46-55 TTC 18 Female 16-25 Bicycle
4 Male 46-55 Car 19 Female 16-25 TTC
5 Female 36-45 Other Method 20 Female 16-25 Walking
6 Female 26-35 Walking 21 Male 36-55 Bicycle
7 Male 26-35 Bicycle 22 Female 16-25 Other Method
8 Female 56-65 TTC 23 Male 56-65 Walking
9 Male 56-65 TTC 24 Female 36-45 Bicycle
10 Male 16-25 Bicycle 25 Male 56-65 Car
11 Male 46-55 TTC 26 Male 46-55 Car
12 Female 46-55 TTC 27 Male 46-55 Bicycle
13 Female 46-55 TTC 28 Male 56-65 Other Method
14 Male 26-35 Bicycle 29 Female 16-25 TTC
15 Male 26-35 Bicycle 30 Female 16-25 Bicycle
Construct the following:
a. a table, b. a simple bar chart, and c. a pie chart to show the mode of
transportation that the 30 people listed above used to commute to work during
the last summer. These 30 people live and work in the GTA.
a. The table shows the mode of transportation that 30 people used to commute
to work during the last summer. These 30 people live and work in the GTA.
Mode of Transportation To Work Number of Respondents
Bicycle 11
Car 3
TTC 9
Walking 4
Other Method 3
b. The simple bar Chart shows the mode of transportation that 30 people used
to commute to work during the last summer. These 30 people live and work in
the GTA.
Fall2012 Page #3 QMS102-Business Statistics I Chapter 2 and 3
c.
Mode of transportation Number of respondents Percent
to Work
Bicycle 11 36.7%
Car 3 10.0%
TTC 9 30.0%
Walking 4 13.3%
Other Method 3 10.0%
The Pie Chart shows the mode of transportation that 30 people used to
commute to work in last summer. These 30 people live and work in the GTA
Fall2012 Page #4 QMS102-Business Statistics I Chapter 2 and 3
10.0%
13.3% 36.7% Bicycle
Car
TTC
Walking
Other Method
30.0%
10.0%
Construct a contingency table and a clustered graph show that the mode of
transportation that the 30 people under study used to commute to work in last
summer and their gender
Title: The contingency table shows the mode of transportation that 30 people
used to commute to work during the last summer and their gender
Mode of Gender
Transportation
Female Male
Bicycle
Car
TTC
Walking
Other Method
Title: The clustered bar chart shows the mode of transportation that 30 people
used to commute to work during the last summer and their gender
Fall2012 Page #5 QMS102-Business Statistics I Chapter 2 and 3
Example2
The following data represent the average values of the U.S. dollars in Canadian
cents for the period 1992 to 2003, reported on a yearly basis by the Bank of
Canada.
Years 1992 1993 1994 1995 1996 1997
U.S.dollars (in Cdn. Cents) 120.8 127.0 136.6 137.2 136.3 138.4
Years 1998 1999 2000 2001 2002 2003
U.S.dollars (in Cdn. Cents) 148.3 148.5 148.5 154.9 157.0 158.0
Construct a single graph to present the above data.
The line graph shows the 120 mutual funds that are classified according to
the risk level of mutual funds.
Fall2012 Page #6 QMS102-Business Statistics I Chapter 2 and 3
160
155
s 150
n
e 145
C
a 140
d 135
a
a 130
C
( 125
a
l 120
d
S 115
U
110
105
100
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Year
Quantitative (Numerical) Data can be organized into
a. Stem-and-Leaf
Fall2012 Page #7 QMS102-Business Statistics I Chapter 2 and 3
b. Array
c. Frequency, Relative Frequency, Cumulative Frequency Distribution
d. Histogram
e. Polygon
f. Ogive (Cumulative Frequency Diagram)
a. Stem-and-Leaf
1. Each numerical value divides into two parts. The leading digit(s) becomes
the stem and the trailing digit the leaf. The stems are located along the
vertical axis, and the leaf values are stacked against each other along the
horizontal axis.
b. Array
1. Arrange the data in ascending or descending order
2. Advantages
a. Identify the lowest and the highest value easily. (range)
b. Identify the most frequently occurring value easily. (mode)
c. Identify the central value easily. (median)
c. Frequency Distribution Table
1.A summary table that divides quantitative data

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