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

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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
Online Homework Link
The student access to the site is:
https://www.ranger.ryerson.ca/qms102ho
mework/
mework/
Module 1 is due on September 20 at
6 a.m.
Other module deadlines are
indicated on the homework
site.
Announcement
Online Homework
Online Homework Link
The student access to the site is:
https://www.ranger.ryerson.ca/qms102ho
mework/
mework/
Module 1 is due on September 20 at 6am
Announcement
Other issues
DO NOT USE my personal email address.
(Note: You will not receive any response if
you send it to my personal account).
USE
fil
USE
qms
ryerson.ca
f
or ema
il
correspondences.
Recommended calculator: CASIO FX-
9750G Plus or CASIO FX-9750GII
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
Nominal Data
classification data, e.g. male/female
no ordering, e.g. it makes no sense to state that Male > Female
– arbitrary labels, e.g., male/female, 0/1, etc
Ordinal Data
– ordered but differences between values are not important
– e.g., political parties on left to right spectrum given labels 0, 1, 2
– e.g., Likertscales, rank on a scale of 1 to 5 your degree of satisfaction
– e.g., restaurant ratings (are preference scores, e.g. ratings of eating
establishments where 10=good, 1=poor)
Interval Data
– ordered, constant scale, but no natural zero
– differences make sense, but ratios do not (e.g., 30°-20°=20°-10°, but 20° /10° is not twice
as hot!
–(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.)
– e.g., temperature (C,F), dates
www.notesolution.com
2
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
.
)
Frequently Asked Questions (FAQ)
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
(00’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
(0’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 ($000’s)
Stem Leaf
1
1
2
2
33
6666789999
023333
7
(0,000,000s)
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 ($000’s)
Stem Leaf
0
111112223
(00,000,000s)
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
(00,000’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)
If positive and
negative numbers are both present, +0 and -0 are used
as stems
For Negative Stem Values
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 – 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 – 1 yr %
Stem Leaf
-
8
1
(0’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
(0’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

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Description
Announcement Announcement QUIZ 1 Quiz 1 is on week 4 (held in class). Check the date on Online Homework Link the handout agenda. The student access to the site is: Topics that will be tested in quiz #1: https:www.ranger.ryerson.caqms102ho i)) Dataypes measurement scales ii) Stem and Leaf Display meewoork Module 1 is due on September 20 at iii) Frequency Distribution 6 a.m. iv) OGIVE Other module deadlines are Format of the Quiz1: Multiple Choice Question indicated on the homework site. Announcement Announcement Online Homework Other issues Online Homework Link DO NOT USE my personal email address. The student access to the site is: (Note: You will not receive any response if https:www.ranger.ryerson.caqms102ho you send it to my personal account). meewoork USSE qms1 [email protected]@ryerson.ca ffor emaiill Module 1 is due on September 20 at 6am correspondences. Recommended calculator: CASIO FX- 9750G Plus or CASIO FX-9750GII TI-83 model is acceptable but I will not be using it in class. Nominal Data Review classification data, e.g. malefemale no ordering, e.g. it makes no sense to state that Male > Female Scales of Measurement arbitrary labels, e.g., malefemale, 01, etc Ordinal Data Data comes in various sizes and shapes and it is ordered but differences between values are not important e.g., political parties on left to right spectrum given labels 0, 1, 2 important to know about these so that the proper e.g., Likert scales, rank on a scale of 1 to 5 your degree of satisfaction analysis can be used on the data. There are e.g., restaurare preference scores, e.g. ratings of eating establishments where 10=)ood, 1=poor usually 4 scales of measurement that must be Interval Data considered: ordered, constant scale, but no natural zero as hot!nces make sense, but ratios do not (e.g., 30- 20=20-10, but 20 10 is not twice 1.Nominal (You are also allowed to quantify the difference between two interval scale values but there is no 2.Ordinal natural zero. For example, temperature scales are interval data with 25C warmer than 20C and a 5C say that 20C is twice as hot as 10C.) Note that 0C is arbitrary, so that it does not make sense to 3.Interval e.g., temperature (C,F), dates 4.Ratio 1 www.notesolution.com Ratio Data - ordered, constant scale, natural zero Frequently Asked Questions (FAQ) What is a natural zero? - e.g., height, weight, age, length Some scales of measurement have a natural zero and -(You are also allowed to take ratios among ratio scaled variables. some do not. Physical measurements of height, weight, length are typically ratio variables. It is now meaningful to say that 10 m is twice as long as For example, height, weight etc have a natural 0 at no height or no weight. 5 m. This ratio hold true regardless of which scale the object is It makes sense to say that 2m is twice as large as 1m. Both of these being measured in (e.g. meters or yards). This is because there is a variables are ratio scale. naturalzeo.)) 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 Stem-and-Leaf Display 1.Measurement Scales Solutions to question 2.10 (page 57) 2.Stem and Leaf Display n.a. Question 2.10 a. Profit Rank n.a Question 2.10 b. Asset Rank 24 34 569 Profit Rank 20 Asset Rank n.a. 48 Highest Stem Leaf Lowest Stem Leaf 3 Lowest (00s) 1 (0s) 15 6 546 0 0000111112223 27 0 1234 19 35 1 0 569 4 2 14 1 124 31 21 n.a 3 n.a 1 4 2 014 27 11 7 5 3467 2 2 7 26 4 3 4 14 44 3 5 533 3 4 4 574 24 4 8 Highest 12 9 11 5 9 12 2 www.notesolution.com
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