presentation chapter 4 mth1022rev#01
TRANSCRIPT
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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
Qualification of DRB Hicom Holdingemployees for year 2009
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Vertical Bar Charts
0
5
10
15
20
25
SPM Certificate Diploma Degree
N
o.ofemployee
s
Qualification
Qualification of DRB Hicom Holdingemployees for year 2009
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Stacked / Component Bar Charts
0
5
10
15
20
25
30
35
40
45
50
SPM Certificate Diploma Degree
N
o.ofemployee
s
Qualification
Qualification of DRB Hicom Holdingemployees for year 2009
2010
2009
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Clustered Bar Charts
0
5
10
15
20
25
30
SPM Certificate Diploma Degree
No.ofemployee
s
Qualification
Qualification of DRB Hicom Holdingemployees for year 2009
2009
2010
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Pie Charts
10, 20%
20, 40%5, 10%
15, 30%
Qualification of DRB Hicom Holdingemployees for year 2009
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