Presentation Chapter 4 MTH1022rev#01

7/28/2019 Presentation Chapter 4 MTH1022rev#01

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TOPIC 4DATA PRESENTATION

Module Outcomes:MO1 Identify basic mathematical concepts, skills and mathematical

techniques for algebra, calculus and data handling.

MO2Apply the mathematical calculations, formulas, statistical

methods and calculus techniques for problem solving in

industry.

MO3 Analyse calculus and statistical problems in industry.


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LEARNING OUTCOMES

At the end of this topic, student should be able to :

differentiate between ungroup and group data

organize data by the ordered array ascending anddescending

clarify the important terms in the construction of frequency

table : class interval, class limit, class boundary, classwidth and class mark

construct a frequency distribution table

portray a frequency distribution in a charts : line charts, bar charts, pie charts

construct histogram and frequency polygon construct a less than cumulative frequency distribution

table

draw an ogive from the less than cumulative frequency

distribution table interpret a practically data presentation


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Introduction

STATISTICS???

STATISTICSPRESENTING

COLLECTING

ORGANIZING

INTERPRETING

ANALYZING


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DATA?

??

Quantitative

Data that can bemeasured

numerically Heights, weights,prices and etc.

Qualitative

Data thatcannot assumenumericalvalue but canbe classified

Color, status,race and etc.

An item of

information

obtained from

variable.


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Data : QUANTITATIVE

QUANTITATIVE

DiscreteAssume

countablevalues

Continuous

Assume any numericalvalue over a certain

interval or in decimalvalues


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VariableCharacteristic of the

population under

study.

Monthly

income

Gender

Level ofeducation

Type of

vehicle


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Example :

Research / Topic of StudyQualification of DRB-Hicom Holding employees for

year 2009.

Variable

Qualification of DRB-Hicom Holding employees

Data

SPM, Certificate, Diploma, Degree, Master


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Population

PopulationThe collection of all elements whose

characteristics are being studied

Sample A portion of population selected by study.


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Random

sample

A sample selected in a

such way that each

element of the

population has some

chance of beingselected


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Data Presentation

An essential step before further statisticalanalysis warranted.

Some common data presentations include: Frequency table

Bar chart Pie chart

Histogram

Frequency curve

Line graph

Pictograph

Ogive

Etc.


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Data presentation of ungrouped

data

Ungrouped data is data obtained inoriginal form are called as raw dataor

data without class interval.

Example: 11, 6, 15, 9 13, 8


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Data Presentation for Ungrouped Data

Table

Qualification No. of

employeesSPM 10

Certificate 20

Diploma 5

Degree 15

Qualification of DRB Hicom

Holding employees for year 2009


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Line Charts

0

5

10

15

20

25

SPM Certificate Diploma Degree

No.ofemplo

yees

Qualification

Qualification of DRB Hicom Holdingemployees for year 2009


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Horizontal Bar Charts

0 5 10 15 20 25

SPM

Certificate

Diploma

Degree

No. of employees

Qualification



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Vertical Bar Charts

0

5

10

15

20

25


N

o.ofemployee

s

Qualification



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Stacked / Component Bar Charts

0

5

10

15

20

25

30

35

40

45

50


N

o.ofemployee

s

Qualification


2010

2009


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Clustered Bar Charts

0

5

10

15

20

25

30


No.ofemployee

s

Qualification


2009

2010


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Pie Charts

10, 20%

20, 40%5, 10%

15, 30%


SPM

Certificate

Diploma

Degree


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How to construct Pie Charts.

Example :

You are given the following data, construct the

Pie Chart.

Qualification No. ofemployees

SPM 10

Certificate 20

Diploma 5

Degree 15


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Solution

1. Calculate degree for each item given.

2. Draw the Pie Chart according degree for each item.

3. Write the legend and title.

Qualification No. of

employees Degree

SPM 10

Certificate 20

Diploma 5

Degree 15

72360

50

10

14436050

20

3636050

5

10836050

15


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Exercise 1

You are given a list of expenditure of an average family per month asfollows:

Draw in your answer paper,(a) Vertical Bar Chart

(b) Pie Chart

(c) Line Chart

Type of Commodity Expenditure (RM)

Food 33

Rent 22

Clothing 10Education 12

Savings 15

Miscellaneous 7


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Exercise 2

You are given a list of expenditure of an average family per month asfollows:

By using Microsoft Office Excel, construct the following charts :(a) Vertical Bar Chart

(b) Pie Chart

(c) Line Chart

Type of Commodity Expenditure (RM)

Food 33

Rent 22

Clothing 10Education 12

Savings 15

Miscellaneous 7

D t t ti f d


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Frequency

distribution of

grouped data

A frequency table summarizes the

data collected by forming intervals

of values and indicating the

number of data falls into each

intervals.

Using frequency distribution

table to present the given data

Data presentation of grouped

data


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Frequency distribution table

Consists of several columns Class intervals

Tally

Frequency of class intervals Class boundaries

Midpoint

Relative frequency


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IMPORTANT!!!!

If the data are given in randomly,

we must identify the number of

classes (k) and the class width of

class intervals


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Finding the number of classes

(k)

= + .

: sample of size


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Finding the class width ()

=

: the number of class size

=

H t t t th


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How to construct the

frequency distribution table

Class

Intervals

Frequency

of class

interval

Class

boundaries

Class

midpoints

Relative

frequenc

y

Set of limits

Example:0-4, 5-9, 10-14,

Use tally process

Example:

||| = 3

|||| = 5|||| || = 7

Class boundary is a value that falls

midway between the upper limit .Example:

Class interval Class

boundary

1 4 0.5 4.5

5 8 4.5 8.5

the middle value of a class interval.

Example:Class

Interval

Class

Boundary

Midpoint

1 4 0.5 4.5 2.5

5 8 4.5 8.5 6.5

9 12 8.5 12.5 10.5

=

Example:

Class

Interval

Class

Boundary

Frequency Relative

Frequency

1 4 0.5 4.5 12 12/25 =

0.48

5 8 4.5 8.5 3 3/25 = 0.12

9 12 8.5 12.5 10 10/25=0.4

Total 25 1


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Example :From a sample of 50 customer complaints to maintenance department, the

following data represent the numbers of days between the receipt of the complaint

and resolution of the complaint:

Q1. Base on the formula k = 1+3.3log n, determine the number of classes and classwidth.

Q2. Base on the answer (i), form a frequency distribution, relative frequency and

cumulative frequency table.

54 5 35 137 27 152 2 123 81 74

27 11 19 126 110 110 29 61 35 94

31 26 5 12 4 165 32 29 28 29

26 25 2 14 13 13 10 5 27 4

52 30 22 36 26 20 23 33 68 31


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SOLUTION

No of class:

= 1 + 3.3 log 50 = 6.6 7

Class Width:

=

=

= 24.7 25


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Exercise

Prices of vehicles sold last month at Perodua Second-hand car are as follows:

20,197 20,372 17,454 20,591 23,65116,587 20,169 32,851 16,251 17,047

21,285 21,324 21,609 15,670 12,546

12,935 16,873 22,251 22,277 25,034

21,533 24,443 16,889 17,004 17,155

16,688 20,657 23,613 17,895 17,203

20,765 22,783 23,661 17,642 18,981

Q1. Base on the formula k = 1+3.3log n, determine the number of classes and classwidth.

Q2. Base on the answer (i), starting with 12,000 as the lower class limit for the first

class and rounding up the class interval to the nearest thousand, form a

frequency distribution, relative frequency and cumulative frequency table.


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Histograms

A histogram is a bar graph of a frequency

distribution.

It consists of a set of vertical bars.

An equal-seized histogram consists of bars

with equal width.

The height of each bar corresponds to the

frequency of the class it represents.


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STEPS TO CONSTRUCT A

HISTOGRAM

ClassBoundaries

Identify class boundariesand frequency for eachclass

Mark Class

Boundaries

Mark at the horizontal

axis (x)

Insertfrequency

Insert at vertical axis(y)

Draw avertical bar

The height for each baris based on thefrequency for each class


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Example :From a sample of 50 customer complaints to maintenance department, the

following data represent the numbers of days between the receipt of the complaintand resolution of the complaint:

Q1. From the above data, construct a histogram.

54 5 35 137 27 152 2 123 81 74

27 11 19 126 110 110 29 61 35 94

31 26 5 12 4 165 32 29 28 29

26 25 2 14 13 13 10 5 27 4

52 30 22 36 26 20 23 33 68 31


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Solution

Class Interval Class Boundaries Class Midpoint Tally Frequency

1 - 25 0.5 - 25.5 13 |||| |||| |||| ||| 18

26 - 50 25.5 - 50.5 38 |||| |||| |||| ||| 18

51 - 75 50.5 - 75.5 63 |||| 5

76 - 100 75.5 - 100.5 88 || 2

101 - 125 100.5 - 125.5 113 || 2

126 - 150 125.5 - 150.5 138 ||| 3

151 - 175 150.5 - 175.5 163 || 2


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0

2

4

6

8

10

12

14

16

18

20

13 38 63 88 113 138 163

Fre

quency

Class Midpoint

Histogram

Frequency


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Polygon Frequency

A frequency polygon is constructing byplotting the midpoints of each class and joining

the points by straight lines.


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0

2

4

6

8

10

12

14

16

18

20

13 38 63 88 113 138 163

Fre

quency

Class Midpoint

Polygon Frequency

Frequency

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Presentation Chapter 4 MTH1022rev#01