2. NATURE OF STATISTICS
STATISTICS – scientific procedures and methods for collecting,
organising, summarising, presenting and analysing data, as
well as obtaining useful information, drawing valid conclusions
and making effective decisions based on the analysis.
Example :
Public health : an administrator might be concerned with the
number of resident contract a new flu virus during a certain year
Education : a researcher might want to know if methods of
teaching are better than olds one
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3. Steps in Statistical problem-solving
1) Identifying the problem or opportunity
2) Gathering available facts
3) Gathering new data
4) Classifying and organizing data
5) Presenting and analyzing data
6) Making a decision
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5. TERM IN STATISTICS
Population : consists of all subjects (human or otherwise)
that are being studied
Sample : group of subjects selected from population
Statistic – summary measure computed from sample data
Parameter – summary measure for the entire population
Census – if the study is carried out using the whole
population
Sample survey – involved a subgroup (or sample) of a
population being chosen
Pilot study – is a study done before the actual fieldwork is
carried out.
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6. Data
Primary data
Data collected from primary source or from sample
Example : interviews the respondents, distribute
questionnaire
Advantages –
1) more accurate and consistent
2)Able to explain how the data are collected
Disadvantages -
1) Requires more time, manpower, high cost
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7. Secondary Data
Data collected from other parties
Example : Bank Negara, Statistics Department
Advantage
1) easily accessible from the internet, journals,
annual report etc.
2) inexpensive, less time to collect
Disadvantage
1) lack accuracy because method of data collection
are not explained
2) biased – original purpose of data collection is not
known
3) not meet the specific needs and objectives
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9. Qualitative : variable that can categorize according to
some characteristic or attribute.
Example : gender (male or female), religious preference
(Muslim, Buddha, Christian)
Quantitative : numerical and can be order or rank.
Example : Age, height, body temperature
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10. Discrete : assume value that can be counted. 0, 1, 2, 3, …
Example : number of children in a family, number of
student in a classroom.
Continuous : assume an infinite number of values
between any two specific values. Usually obtained by
measuring. Include fractions and decimals
Example : weight, height, time, mass, etc.
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11. Scale of measurement
Nominal scale – categorical data
o The number in the data cannot be added or subtracted
from another number.
o Example: gender (male, female), religion (muslim,
christian, hinduism)
Ordinal scale – can be arranged in ranking order and
inequality signs can be used when comparing the value of
the variable.
o Example: size of building (small, medium, large),
education level (Phd, Master, Degree, Diploma)
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12. Cont..
Interval scale – the differences between data value are
meaningful but cannot be manipulated with multiplication
and division.
o Example: IQ score, temperature
Ratio scale – is the interval measurement with an inherent
zero setting.
o Example: height, weight, time taken to complete a given
task, monthly income.
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14. Non-Probability Sampling Techniques
Convenience sampling
pre-testing of questionnaires
Judgemental Sampling
selected based on the judgement
Snowball Sampling
select respondent at random. After interviewed, asked
respondent to identify others who are in the target
population of interest
Quota Sampling
observes the specific characteristics of potential
respondent.
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15. Simple random sampling
each item have the same chance of being selected as a
sample
Systematic sampling
Samples are selected by using every kth number after the
first subject is randomly selected from 1 through k
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Probability Sampling Techniques
16. Stratified sampling
divide the population into groups (strata) and samples selected
randomly within groups
Example:
A factory manager wants to find out what his workers think about the
factory canteen facilities. He decides to give a questionnaire to a sample
of 80 workers. It is though that different age groups will have different
opinions.
There are 75 workers between 18 and 32, 140 workers between 33 and 47
and 85 workers between 48 and 62.
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Probability Sampling Techniques
17. Cluster
divide population into subpopulations or clusters.
Multi-stage sampling
This method is designed to reduce time and cost when
working with samples from very large populations.
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Probability Sampling Techniques
18. Data Collection Methods
Face-to-face interview
Telephone interview
Direct questionnaire
Mail (or postal) questionnaire
Direct observation
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19. Designing a questionnaire
In designing a questionnaire, the following points
should be taken into consideration.
The questionnaire should be short and simple
Begin with simple and less controversial questions first
Should not be biased towards certain groups
Avoid sensitive questions
A questionnaire checklist can be constructed to ensure
all required data are included.
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iam/ppssp/fskm/2013
21. Organizing and graphing qualitative data
Example 1
Twenty-five army inductees were given a blood test to
determine their blood type. The data set is
A B B AB O
O O B AB B
B B O A O
A O O O AB
AB A O B A
Construct a frequency distribution for the data
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1)Frequency distribution
23. 2) Pie Chart
A pie graph is a circle that is divided into sections or
wedges according to the percentage of frequencies in
each category of the distribution.
Procedure for constructing a pie chart : Refer to
Example 1
Step 1: Number of categories = 4
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24. Step 2 : Percentage
Step 3 : Convert to degrees (total 360)
%
16
100
25
4
:
%
36
100
25
9
:
%
28
100
25
7
:
%
20
100
25
5
:
AB
O
B
A
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100
n
f
o
o
o
o
o
o
o
o
AB
O
B
A
6
.
57
360
%
16
:
6
.
129
360
%
36
:
8
.
100
360
%
28
:
72
360
%
20
:
26. 3) Bar Chart
A graph of bars whose heights represent the
frequencies of respective categories
Categories on the vertical axis
Frequencies on the horizontal axis.
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29. 3b) Stacked/component bar chart
Example 2
A random sample of car owners was selected and the
following results were obtained.
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Car ownership City Town Rural
Owns a foreign car 90 60 25
Do not own a foreign car 110 90 125
Total 200 150 150
30. Solution
% of car ownership City Town Rural
Owns a foreign car 45 40 16.7
Do not own a foreign car 55 60 83.3
Total 100 100 100
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0%
20%
40%
60%
80%
100%
City Town Rural
Percentage of car ownership
Do not own a
foreign car
Owns a foreign
car
31. 4) Contingency table
Also known as cross tabulation.
To examine the categorical responses in term of two
qualitative variables simultaneously.
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Red Green White Black Total
Men 30 10 26 34 100
Women 8 10 45 37 100
Total 75 18 63 44 200
32. 2-32
1) Stem-and-Leaf Plots
This plot separates data entries into leading digits and
trailing digits.
Steps
a) Split each value into two sets of digits.
b) List all the possible stem digits from the lowest to the
highest.
c) For each score in the mass of data, write down the leaf
numbers on the line labelled by the appropriate stem
number.
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Organizing and graphing quantitative data
33. Example 3
Display the following data with a stem-and-leaf plot.
3.4 4.5 2.3 2.7 3.8 5.9 3.4 4.7 2.4 4.1 3.6 5.1
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34. Example 4
Construct a stem and leaf plot by using classes 0-4, 5-9,
10-14, 15-19, and 20-24
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3 9 14 22 11 4 12 0
15 20 8 7 5 1 7 13
9 8 14 11 19 17 3 6
35. 2) Histogram
Histogram – graph that
displays the data by using
contiguous vertical bars
(unless the frequency of a
class is 0) of various
heights to represent the
frequencies of the classes.
0
2
4
6
8
0 10.5 20.5 30.5 40.5 50.5 60.5 70.5 80.5
Class Boundaries
Frequency
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36. Example 5
The table below shows the weight of 100 honeydews
produced from Farm X. Draw a histogram representing
the weight distribution of the honeydews.
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Weight (‘00 g) Frequency
4 – 6 4
6 – 8 9
8 – 10 34
10 – 12 25
12 - 14 28
37. 3) Frequency polygon
If a histogram is available, the frequency polygon is
obtained by connecting the mid-point of the tops of
the rectangles in the histogram.
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38. 4) Cumulative frequency distribution
and ogives
Cumulative frequency distribution
There are 2 types of cumulative frequency distributions. They
are ‘less than’ and ‘more than’ cumulative distribution. The
‘less than’ cumulative frequency is more frequently used.
Ogives (Cumulative frequency curve)
Ogive is a graph or line chart of a cumulative frequency
distribution. There are 2 types of ogives. They are ‘less than’
ogive and ‘more than’ ogive.
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39. Example 6
The table below shows the number of service years of 120
employees at a firm called SITI. Draw a ‘less than’ ogive.
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Service years No of employees
1 – 4 16
5 – 8 20
9 – 12 28
13 – 16 24
17 – 20 16
21 – 24 11
25 – 28 5
40. Solution
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Service years Cumulative frequency
Less than 0.5 0
Less than 4.5 16
Less than 8.5 36
Less than 12.5 64
Less than 16.5 88
Less than 20.5 104
Less than 24.5 115
Less than 28.5 120
