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QMS 102 (188)
Clare Chua (18)
Lecture

Lecture 4

8 Pages
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Department
Quantitative Methods
Course Code
QMS 102
Professor
Clare Chua

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1
Announcement
Quiz 1 marks will be posted on BB in one-week time
Matter related to online homework
Each online homework is worth 0.45%.
I urge you to focus more on the other evaluation
components as well.
•.
ComponentPercent/Weight
Quiz #1
10%
The online homework is designed to help you master the
concepts.
Read the instructions carefully.
Quiz #1
10%
Test 25%
Quiz #2 10%
11 Online
homework 5%
Final Exam50%
Lecture 4
Measure of Central Tendency
1. What are the measures of Location?
2. How to compute mode?
3H t t
di
?
3
.
H
ow
t
o compu
t
e me
di
an
?
4. How to compute mean?
5. How to use the Casio calculator to obtain
the mean, median and mode?
Learning Objectives
By the end of this module, you will be able to
Calculate mode with raw data and grouped
data.
Calculate median with raw data and grouped
Calculate
median
with
raw
data
and
grouped
data.
Calculate mean with raw data and grouped
data.
3.1 Descriptive Statistics 1:
Measures of Central Tendency
page 130
page
130
Mean
Median
Mode
Bank
Name
Minimum
Deposit to
Open
Minimum
Balance to
avoid Fee
Monthly
Service
Charge Bounced
Check Fee Foreign
ATM Fee
Online
Account
Access
What are Data?
Newton Federal $100.00 $500.00 $12.00 $22.00 $1.00 No
Bank of North Georgia $100.00 $1,000.00 $8.00 $24.00 $0.00 No
Herita
g
e$50.00 $500.00 $5.00 $25.00 $0.00 No
g
Middlesex Savings $1.00 $1,000.00 $5.00 $15.00 $0.00 No
Cambridge Savings $10.00 $1,000.00 $6.00 $20.00 $1.00 Yes
Mid America$50.00 $500.00 $6.00 $21.00 $1.50 Yes
LaSalle $100.00 $750.00 $10.00 $22.00 $1.50 Yes
Guaranty Federal $100.00 $1,000.00 $10.00 $20.00 $1.50 Yes
Bank One, Texas$100.00 $800.00 $9.00 $25.00 $1.25 Yes
Bank of America$25.00 $500.00 $7.00 $25.00 $1.25 Yes
Compass$100.00 $750.00 $10.00 $25.00 $1.00 Yes
FirstBank of Colorado $500.00 $500.00 $7.00 $15.00 $1.00 Yes
Recap of what you have learned?
Making Data Informative
Organizing Stem and Leaf Display
Frequency Distribution
Present
Describe
Analyze
(Relative/Percent)
OGIVE
Chapter 2
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2
Today's LECTURE ON….
Organizing
Present
Describe
Chapter 3 (page 130):
Numerical Descriptive
Measures (Descriptive
t
ti
ti
)
Describe
Analyze
)
Measures of
Central Tendency
Measures of
Variability
A single Value to
represent the data
Set.
A single Value to
describe how
Spread the data is.
What are the Measures of
Central Tendency?
Given a set of quantitativedata:
1. where is the “center” (or middle) of this
set of data?
2. The “center” of a bunch of data values
can be described as asingle value
can
be
described
as
a
single
value
.
3. This computation of a single value is
called the measure of central tendency or
measure of location.
Most common measures of the center of
the data are mode, median and mean.
Illustration of the “center” of the
data set.
A random sample of 12 students who have taken QMS102 quiz 1.
The quiz 1 contains 10 multiple choice questions. Each
question is worth one mark. The following are the distribution
of marks for 11 students:
1, 1, 3, 4, 5, 5, 5, 5, 5, 5, 8, 10.
012345678910
Quiz1Score
where is the center (or middle value) of the data?
Illustration of the “center” of the
data set.
A random sample of 12 students who have taken QMS102 quiz 1.
The quiz 1 contains 10 multiple choice questions. Each
question is worth one mark. The following are the distribution
of marks for 11 students:
1, 1, 3, 4, 5, 5, 5, 5, 5, 5, 8, 10.
012345678910
Quiz1Score
Numerical measures:
Mean=4.75
Mode=5
Median=5
where is the center (or middle value) of the data?
. You need some proper measure to confirm this
Measures of Central Tendency
Measures Central Tendency
MODE
MEDIAN
MEAN
MODE
MEDIAN
MEAN
Read page 140
Note: Use the calculator to calculate the mode
How to compute mode?
MODE:Mode requires no mathematical calculation to
obtain its value.
The mode is the value corresponding to the highest
frequencyin a data set.
Example 1: One mode
The following are the
scores for 12 students: 1, 1, 3, 4, 5, 5, 5, 5, 5, 5, 8, 10.
The dot diagram shows the distribution of the scores for the 12 students.
What is the mode value?
The mode is 5 because this value has the highest frequency (i.e. it occurs 6 times)
ONEmode
0 1 2 3 4 5 6 78910
Quiz1Score
Mode
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3
Measures of Central Tendency
MODE
Example: Quiz #1 Scores
What is the MODE?
01
2345678910
EXAMPLE 2: No mode
The following are the scores for 11 students:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The dot
diagram shows the distribution of the
scores for the 11 students
scores
for
the
11
students
.
Quiz1Score
012345678910
What is the mode in this set of data?
Answer: There is no mode
EXAMPLE 3: Multimodal
The following are the scores for 11 students: 2, 3, 4, 4, 5,
6, 6, 8, 8, 10, 10. The dot diagram shows the distribution
of the scores for the 11 students.
012345678910
Q
uiz1Score
ModeMode
ModeMode
What is the mode value in this set of data?
Answer: There are four modes; 4, 6, 8 and 10
because each of these values occurs twice.
Measures of Central Tendency
Measures Central Tendency
MODE
MEDIAN
MEAN
MODE
MEDIAN
MEAN
MEDIAN:The median is the middle position of the data
after it is sorted into an ordered array.
Read page 138
Note: Use the calculator to calculate the median.
How to compute median?
Example: Quiz #1 Scores
What is the MEDIAN?
01
2345678910
01112222 334
How to compute median?
Example: Quiz #1 Scores
What is the MEDIAN?
01
2345678910
01112222 334
1
POSITION 23
45678910 11
Where is the middle position?
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Description
Announcement Quiz 1 marks will be posted on BB in one-week time Lecture 4 Matter related to online homework Each online homework is worth 0.45%. Measure of Central Tendency I urge you to focus more on the other evaluation components as well. 1. What are the measures of Location? . Compon en t Percen tWe igh t 2. How to compute mode? Qu i#11 # 10% Test 25% 3. How tto computet med diian?? Qu iz #2 10% 4. How to compute mean? 11 On lin e 5% ho m ew ork 5. How to use the Casio calculator to obtain Fina l Exa m 50% the mean, median and mode? The online homework is designed to help you master the concepts. Read the instructions carefully. Learning Objectives By the end of this module, you will be able to Calculate mode with raw data and grouped 3.1 Descriptive Statistics 1: data. Measures of Central Tendency Caalcuulatte meeddiann wiith raww ddaata aandd grrouupeed pagge 1330 data. Mean Calculate mean with raw data and grouped data. Median Mode What are Data? Recap of what you have learned? Minimum Minimum Monthly Online Bank Deposit to Balance to Service Bounced Foreign Account Name Open avoid Fee Charge Check Fee ATM Fee Access Making Data Informative Newton Federa$100.00 $500.00 $12.00 $22.00 $1.00 No Organizing Stem and Leaf Display Bank of North$100.00a $1,000.00 $8.00 $24.00 $0.00 No Herita $50.00 $500.00 $5.00 $25.00 $0.00 No Frequency Distribution Middlesex Savi$1.00 $1,000.00 $5.00 $15.00 $0.00 No Present (RelativePercent) Cambridge Savi$10.00 $1,000.00 $6.00 $20.00 $1.00 Yes Mid America $50.00 $500.00 $6.00 $21.00 $1.50 Yes OGIVE LaSalle $100.00 $750.00 $10.00 $22.00 $1.50 Yes Guaranty Fede$100.00 $1,000.00 $10.00 $20.00 $1.50 Yes Describe Bank One, Tex$100.00 $800.00 $9.00 $25.00 $1.25 Yes Chapter 2 Bank of Americ$25.00 $500.00 $7.00 $25.00 $1.25 Yes Compass $100.00 $750.00 $10.00 $25.00 $1.00 Yes Analyze FirstBank of $500.00o $500.00 $7.00 $15.00 $1.00 Yes 1 www.notesolution.com
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