Class Notes (906,593)
CA (538,683)
Ryerson (30,392)
QMS (276)
QMS 102 (188)
Clare Chua (18)
Lecture

# Lecture 2

14 Pages
131 Views

Department
Quantitative Methods
Course Code
QMS 102
Professor
Clare Chua

This preview shows pages 1-3. Sign up to view the full 14 pages of the document.
1
Announcement
QUIZ 1
Quiz 1 is on week 4 (held in class). Check the date on
the handout agenda.
Topics that will be tested in quiz #1:
i
)
Data t
yp
es/ measurement scales
)yp
ii) Stem and Leaf Display
iii) Frequency Distribution
iv) OGIVE
Format of the Quiz1: Multiple Choice Question
Announcement
https://www.ranger.ryerson.ca/qms102ho
mework/
mework/
â€¢Module 1 is due on September 20 at
6 a.m.
indicated on the homework
site.
Announcement
Online Homework
https://www.ranger.ryerson.ca/qms102ho
mework/
mework/
â€¢Module 1 is due on September 20 at 6am
Announcement
Other issues
â€¢DO NOT USE my personal email address.
(Note: You will not receive any response if
you send it to my personal account).
USE
fil
â€¢
USE
qms
ryerson.ca
f
or ema
il
correspondences.
â€¢Recommended calculator: CASIO FX-
9750G Plus or CASIO FX-9750GII
â€¢TI-83 model is acceptable but I will not be
using it in class.
Review
Scales of Measurement
Data comes in various sizes and shapes and it is
important to know about these so that the proper
analysis can be used on the data. There are
usually 4 scales of measurement that must be
considered:
1.Nominal
2.Ordinal
3.Interval
4.Ratio
â€¢Nominal Data
â€“classification data, e.g. male/female
â€“no ordering, e.g. it makes no sense to state that Male > Female
â€“ arbitrary labels, e.g., male/female, 0/1, etc
â€¢Ordinal Data
â€“ ordered but differences between values are not important
â€“ e.g., political parties on left to right spectrum given labels 0, 1, 2
â€“ e.g., Likertscales, rank on a scale of 1 to 5 your degree of satisfaction
â€“ e.g., restaurant ratings (are preference scores, e.g. ratings of eating
establishments where 10=good, 1=poor)
â€¢Interval Data
â€“ ordered, constant scale, but no natural zero
â€“ differences make sense, but ratios do not (e.g., 30Â°-20Â°=20Â°-10Â°, but 20Â° /10Â° is not twice
as hot!
â€“(You are also allowed to quantify the difference between two interval scale values but there is no
natural zero. For example, temperature scales are interval data with 25C warmer than 20C and a 5C
difference has some physical meaning. Note that 0C is arbitrary, so that it does not make sense to
say that 20C is twice as hot as 10C.)
â€“ e.g., temperature (C,F), dates
www.notesolution.com
2
â€¢Ratio Data
-ordered, constant scale, natural zero
-e.g., height, weight, age, length
-(You are also allowed to take ratios among ratio scaled variables.
Physical measurements of height, weight, length are typically ratio
variables. It is now meaningful to say that 10 m is twice as long as
5 m. This ratio hold true regardless of which scale the object is
being measured in (e.g. meters or yards). This is because there is a
natural
zero)
natural
zero
.
)
What is a natural zero?
Some scales of measurement have a natural zero and
some do not.
For example, height, weight etc have a natural 0 at no height or no weight.
It makes sense to say that 2m is twice as large as 1m. Both of these
variables are ratio scale.
On the other hand, year and temperature (C) do not have a natural zero.
The year 0 is arbitrary and it is not sensible to say that the year 2000 is twice as old
as the year 1000.
Similarly, 0C is arbitary (why pick the freezing point of water?)
and it again does not make sense to say that 20C is twice as hot as 10C.
Both of these variables are interval scale.
We have covered two
topics in Lecture 1
1.Measurement Scales
2.Stem and Leaf
Display
Stem-and-Leaf Display
Solutions to question 2.10 (page
57)
Question 2.10 a. Profit Rank
n.a.
24
569
n.a.
3
15
546
19
4
31
Profit Rank
Stem Leaf
0
1
2
3
0000111112223
(00â€™s)
Lowest
n.a
27
7
26
14
533
574
12
11
9
3
4
5 3467
Highest
Question 2.10 b. Asset Rank
n.a
34
20
48
1
6
27
35
14
21
Asset Rank
Stem Leaf
0
0
1
1
1234
569
124
(0â€™s)
Lowest
Highest
n.a
11
2
4
44
3
24
9
5
12
1
2
2
3
3
4
4
014
7
4
5
4
8
www.notesolution.com
3
Question 2.10 c. Revenues for 2002
37,000,000
27,446,000
23,664,900
23,328,700
23,234,000
23,101,000
22,653,000
20,364,470
19,768,000
19
687
800
Revenue 2002 â€“(\$000â€™s)
Stem Leaf
1
1
2
2
33
6666789999
023333
7
(0,000,000â€™s)
Highest
19,353,000
19,017,000
18,310,000
17,055,000
16,890,000
16,680,000
16,538,380
16,532,000
13,059,000
13,002,000
2
3
3
7
7
Lowest
Question 2.10 d. Assets for 2002
n.a.
16,630,000
29,009,400
11,398,000
376,956,000
123,438,000
19,890,000
16,004,076
39,563,000
27
,
674
,
964
Assets 2002 â€“(\$000â€™s)
Stem Leaf
0
111112223
(00,000,000â€™s)
Lowest
Highest
,,
n.a.
70,136,000
296,380,000
273,293,000
11,868,000
278,040,000
23,382,804
81,195,000
252,864,000
59,078,000
0
0
1
1
2
2
3
3
111112223
578
2
5779
7
Question 2.10 e. Number of Employees
24,500
139,000
75,000
15,074
59,549
11,800
98,000
73,000
66,266
50
,
000
Number of Employees
Stem Leaf
0011
(00,000â€™s)
Highest
,
n.a.
28,000
49,000
42,552
6,460
42,817
52,600
32,400
33,000
20,972
0
0
0
0
1
1
22233
444555
677
9
3
Lowest
Stem and lea
f
display with
negative and positive numbers
(page 53)
â€¢If positive and
negative numbers are both present, +0 and -0 are used
as stems
â€¢For Negative Stem Values â€“
Repeat stem
Leaves
Repeat Stem
Leaves
Repeat
stem
twice
Leaves
Values
Repeat
Stem
five times
Leaves
Values
First Stem 5-9 1st Stem 8-9
Second Stem 0-4 2nd Stem 6-7
3rd Stem 4-5
4th Stem 2-3
5th Stem 0-1
Remember for positive numbers: The leaves are written in ascending orderascending order.
for negative numbers: The leaves may be written in descending orderdescending order
Question 2.10 f. Share Price Change â€“ 1
year percent
n.a.
(19.4)
(81.1)
n.a.
9.2
(17.6)
(36.9)
(32.8)
(2.3)
(
33.1
)
Share Price Change â€“ 1 yr %
Stem Leaf
-
8
1
(0â€™s)
Lowest
Highest
()
n.a.
(5.9)
(0.5)
(15.7)
(0.7)
(24.3)
(56.3)
(18.5)
4.9
n.a.
8
-7
-6
-5
-4
-3
-2
-1
-0
0
1
6
632
4
9875
520
49
for negative numbers:
The leaves may be written
in descending orderdescending order
for positive numbers:
The leaves may be written
in ascending orderascending order
Question 2.10 g. Profit as a percent of
Assets
n.a.
4.2
(2.2)
n.a.
0.8
1.0
(0.7)
6.1
5.3
2.1
Profit as a % of Assets
Stem Leaf
-
1
9
(0â€™s)
for negative stems:
9
n.a.
0.9
0.6
0.2
10.7
n.a.
(19.9)
1.7
0.6
2.6
1
-1
-0
-0
0
0
1
9
20
0000011224
56
0
Lowest
Highest
leaves value 5-
9
go to the
first stem; 0-4 go to the
second stem.
for positive stems:
leaves values 0-4
go to the first stem,
55--9 go to the second 9 go to the second
stemstem
www.notesolution.com

#### Loved by over 2.2 million students

Over 90% improved by at least one letter grade.

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah â€” University of Toronto

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim â€” University of Michigan

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna â€” University of Wisconsin

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne â€” University of California
Description
More Less

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Unlock Document

Unlock to view full version

Unlock Document
Notes
Practice
Earn
Me

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.