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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

S

t

a

ti

s

ti

cs

)

Describe

Analyze

Sa s cs

)

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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