Methods for Presentation of Data

1. THE UNIVERSITY OF AZAD JAMMU & KASHMIR
MUZAFFARABAD
Social Statistics
Assignment No. 01
Submitted to:
Sir Atif Abbasi
Submitted by:
Waheed Ahmad Qureshi
Roll No. 67
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2. Q. No.1: Discuss the different methods for the presentation of Data with Examples.
Methods for the Presentation of Data
Introduction:
Data may be collected through different sources. It is difficult to learn anything by examining
the un-organized data which is more often confusing than clarifying. The mass of data is
therefore to be organized and condensed into a form that can be easily understood and
interpreted. For this purpose techniques of classification, tabulation and graphic displays are
introduced.
Data:
Data is the collection of facts from which the conclusion may be drawn. It is further classified
into two types:
1. Primary Data
2. Secondary Data
Presentation of Data:
The methods which are used for the presentation of data are as under:
1. Classification
2. Tabulation
3. Graphical Representation
4. Diagrammatic Representation
1. CLASSIFICATION:
One of the methods of the Presentation of data is classification. It is a process of
dividing a set of observations or objects into classes or groups in such a way that:
i. Observations or objects in the same class or group are similar.
ii. Observations or objects in each class or group are dissimilar to the other
groups.
Definition:
“The process of arranging data into classes or categories according to some common
characteristics present in the data is called classification”. e.g. attributes, weights,
geographical characteristics etc.
Examples:
i. The population of country may be classified by religion as Muslim,
Christians, and Hindus etc.
ii. If in a primary school examination, we have the results of 1000 students, it
is difficult to tell. Similarly, by looking at the marks, as how many
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3. students obtained marks from 350 to 449, 450 to 549, 550 to 659 and so
on. Now if we arrange the data and make the groups and find out number
of students in each group. It is easy to understand.
Basis of classification:
Although data can be classified by many characteristics but there are four
important basis for classification of data
Qualitative:
When data are classified by attributes, e.g., sex, religion,, martial status,
morality, friendship etc.
Quantitative:
When data are classified by quantitative characteristics, e.g., heights, weights,
age, speed etc
Spatial or Geographical:
When data are classified by geographical region or location e.g., the
population of a country may be classified by provinces, divisions, districts or
towns
Chronological or Temporal:
When data are classified by their time of occurrence such arrangement is
called a time series.
Basic principals of classification:
While classifying large sets of data, the following points should be taken into
consideration
• The classes or categories, into which the data are to be divided, should be
mutually exclusive and no overlap should exist between successive
classes. In other words, classes should be arranged so that each
observation or object can be placed in one and only one class.
• The classes or categories should be all inclusive. All inclusive classes are
classes that include all the data.
• As far as possible, the conventional classification procedure should be
adopted.
• The classification procedure should not be so elaborate as to lead to trivial
classes nor should it be so crude as to concentrate all the data in one or two
classes.
2. TABULATION:
Statistical table is a systematic arrangement of data into vertical columns and
horizontal rows. The process of arranging data into rows and columns is called
tabulation. According to Prof. Bowely, “Tabulation is the intermediate process
between the accumulations of data, in whatever form they are obtained and the final
accounts of the results shown by the statistics”.
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4. Tabulation may be:
Simple
When tabulation is done according to one way classification, like the population of a
country is classified according to religion or marital status, called simple
classification.
Double
When tabulation corresponding to two way classification, such as tabulation of data
classified by religion and sex or religion and material status is an example of double
tabulation.
Complex
When tabulation is done by many-way classification, it is called complex tabulation.
An example of complex tabulation is the presentation of data on the population of a
country classified by age, sex, religion and marital status etc.
Main Parts of Table:
As statistical table has at least four parts – the title, stub, head and body. In addition,
some tables have one or more prefatory notes, a foot note and a source note. All these
are shown in the following Table:
Population of Punjab and Baluchistan provinces by sex for 1961 and 1972 censuses1
Punjab Baluchistan
Census
Male Female Total Male Female Total
1961 1364 19938 2558 640 521 1161
3 1
1972 1994 17566 3750 1272 1133 2405
2 8
A description of there parts are given below:
Title:
Every table must have title; it should be brief, clearly worded and self explanatory.
The title should describe
a. what the data represents
b. where the data come from
c. how the data have been classified
d. where the data were observed
Column, Captions and Box Head
The heading of a column is called a column caption and the section or parts of the
table containing the column caption is known as box head. The captions should
clearly defined and written in the centre of the columns.
Row Captions and Stub
1
Population census reports, 1961 and 1972
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5. The heading or title of a row is called the row caption and the section of the table
containing row captions is known as stub.
Prefatory Notes and Foot Notes
Both these notes are used to explain certain characteristics of the data. They give
additional specification of the data.
a. The prefatory notes appear between the title and the body.
b. A foot note appears immediately below the body of the table.
3. GRAPHICAL REPRESENTATION
Visual display of statistical data in the form of points, lines, areas and other
geometrical forms and symbols is the most general term known as graphical
representation of data.
Statistical data can be studies with this method without going through figures
presented in the form of tables.
Graph
It is in the form of continuous curve, shown on a graph paper.
Diagram
It Is in the form of one, two or three dimensional or in pictorial form.
Types of diagrams or charts
Following types of diagrams are in common use
One dimensional diagrams or charts
These diagrams have only one dimension. They are used to represent data not having
large variations. It consists of
• Simple bar diagram or chart.
• Multiple bar diagram or chart
• Sub divided bar diagram or component chart.
Simple Bar Diagram or Chart
This chart consists of vertical or horizontal bars of equal width. The length of bars is
taken proportional to the magnitude of the values presented.
Example
Draw simple bar chart to represent the production of wheat in Pakistan during the
years 1971 to 1976
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6. Year 1971 1972 1973 1974 1975 1976
Production
55 60 72 69 69 72
(lake tons)
lakh tons
80
70
60
50 wheat
40
30
20
10
0
1971
1972
1973
1974
1975
1976
Simple bar chart showing production of wheat in Pakistan for the years 1971 to 1976
Multiple Bar Charts
It is an extension of simple bar chart. In this chart grouped bars are used to represent
related set of data. For example, we may represent the imports of a country for a
number of years by means of multiple bars chart, taking groups of 2 bars each--- one
representing imports and the other representing exports. Each bar in a group is shaded
or colored differentially for distinction. Similarly it may have more than 2 groups of
data
Example; draw a multiple bar chart to represent the imports and exports of Pakistan
(value in crores of rupees ) for the year 1970-71 to 1974-75
Years Imports Exports
1970-1971 370 200
1971-1972 350 337
1972-1973 840 855
1973-1974 1438 1016
1974-1975 2092 1029
Source: state bank of Pakistan
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7. 2500
2000
1500
Imports
Exports
1000
500
0
1970-1971 1971-1972 1972-1973 1973-1974 1974-1975
Multiple bar chart showing Imports and Exports of Pakistan from 1970-71 to 1974-75
Sub Divided or Component Bar Chart
This chart is used when it is desired to present data which are subdivisions of totals.
Since the bars show the various component parts, it is also called component bar
charts. In this charts simple bars are drawn with lengths proportion to the totals and
then sub divided in to the parts in the ratio of their components. The components or
shaded or colored differentially so as to distinguish differ parts.
Example: Draw sub divided bar diagram to represent the male and female population
of five divisions of Pakistan in 1961.
Division Male Female Both Sexes
Bahawalpur 14 12 26
Rawalpindi 21 19 40
Sargodha 32 28 60
Lahore 35 30 65
Multan 35 31 66
Source: Population census Report, 1961.
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8. 70
60
50
40
Female
Male
30
20
10
0
1 2 3 4 5
Sub-divided bar graph showing male & female population of five divisions of
Pakistan in 1961
Pie charts
Like the rectangles, circles can also be used to represent and compare data having
large variation. Circles are drawn with radius proportional to the square roots of
quantities to be represented (because the area of a circle is given by 2πr2). Circles are
sub divided into sectors when the totals and their sub divisions have to be compares.
The sectors are shaded or colored differentially. This diagram is used for the same
purpose as the sub divided rectangles however it is difficult to compare areas visually.
For this reason this an inferior form of presentation. The titles describing each
component part should be written in each sector.
To construct a pie chart draw a circle with some suitable radius we know that a circle
consists of 360°. To show the components pair by sectors we calculate the angles for
each sectors by the formula.
The circle is divided in to different sectors by constructing angles at the centre by
means of a protractor. The arrangement of the sectors is generally clock wise.
Example: Draw a pie chart to show the distribution
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9. Academic Number of Cumulative
Angles of sectors
qualification Employees Angles
No Education 47 (47/296) x 360°= 57° 57°
Primary 25 (25/296) x 360°= 30° 87°
Middle 63 77° 164°
Matric 97 118° 282°
Intermediate 26 32° 314°
Bachelor 23 28° 342°
Master 15 18° 360°
Total 296 360
Sources: Census of Punjab government Employees
'Punjab Government Employees by Academic
Qualification'
No Education
Primary
Middle
Matric
Intermediate
Bachclor’s Degree
Master’s Degree
Graphs:
As we know, the diagrams are useful for representing spatial series. Diagrams fail
when we want to represent a statistical series spread over a period of time, or a
frequency distribution or two related variables in visual form. For such
representations, graphs are employed.
Graphs present the data in a simple, clear and effective manner, facilitate comparison
between two or more than two statistical series and help us in appreciating their
significance readily. Graphs can be divided into two main categories, namely:
i. Graph of time series
ii. Graphs of frequency distribution
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10. Example:
Draw a histogram to represent production of cigarettes in Pakistan for the year 1959
to 1968
1959- 1960- 1961- 1962- 1964- 1965- 1966- 1967- 1968-
Year
60 61 62 63 65 66 67 68 69
Production 928 1088 1326 1456 1767 1984 2445 3205 3493
4000
3500
3000
2500
2000
1500
1000
500
0
1959-60 1960-61 1961-62 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68
A histogram consists of a set of adjacent rectangles having bases along the X-axis
(marked off by class boundaries) and areas proportional to the class frequencies. If the
class interval sizes, are equal the heights of the rectangles are also proportional to the
class frequencies if the class interval sizes are not equal, then the heights of the
rectangles have to be adjusted.
Histogram for Frequency Distribution of Annual Death Rates
Class Boundaries Frequency
3.45 – 4.45 1
4.45 – 5.45 4
5.45 – 6.45 5
6.45 – 7.45 13
7.45 – 8.45 12
8.45 – 9.45 19
9.45 – 20.45 13
10.45 – 11.45 10
11.45 – 12.45 6
12.45 – 13.45 4
13.45 – 14.45 1
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11. Academic Number of Cumulative
Angles of sectors
qualification Employees Angles
No Education 47 (47/296) x 360°= 57° 57°
Primary 25 (25/296) x 360°= 30° 87°
Middle 63 77° 164°
Matric 97 118° 282°
Intermediate 26 32° 314°
Bachelor 23 28° 342°
Master 15 18° 360°
Total 296 360
Sources: Census of Punjab government Employees
'Punjab Government Employees by Academic
Qualification'
No Education
Primary
Middle
Matric
Intermediate
Bachclor’s Degree
Master’s Degree
Graphs:
As we know, the diagrams are useful for representing spatial series. Diagrams fail
when we want to represent a statistical series spread over a period of time, or a
frequency distribution or two related variables in visual form. For such
representations, graphs are employed.
Graphs present the data in a simple, clear and effective manner, facilitate comparison
between two or more than two statistical series and help us in appreciating their
significance readily. Graphs can be divided into two main categories, namely:
i. Graph of time series
ii. Graphs of frequency distribution
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