Presentation of Data
11th – D ( 2nd shift )
1) Presentation of Data
1.1) Tabular presentation
1.1.a) Components of table
1.1.b) Features of a good table
1.1.c) Kind of tables
1.1.d) Classification of data and
1.2) Textual presentation
1.3) Diagrammatic presentation
1.3.a) Bar diagrams
1.3.a.i) Types of Bar diagrams
1.3.a.i.A) Simple Bar diagrams
1.3.a.i.B) Multiple Bar diagrams
1.3.a.i.C) Sub-divided Bar diagrams
1.3.a.i.D) Percentage Bar diagram
1.3.b) Pie diagram
1.3.c) Frequency Diagrams
1.3.c.iii) Frequency curve polygon
1.3.c.iv) Ogive or Cumulative
1.3.c.iv.A) Less than Ogive
1.3.c.iv.B) More than Ogive
2.) Some Questions
2.1) Very Short Answer Type
2.2) Short Answer Type Questions
2.3) Long Answer Type Questions
2.4) Numerical Questions
Presentation of Data
The presentation of data means
exhibition of the data in such a clear
and attractive manner that these
are easily understood and analysed.
There are many forms of
presentation of data.
Presentation of Data
1.1 Tabular Presentation
In the process of Tabular
presentation is Data is organized
in rows and columns, this process is
known as tabular presentation.
The method used is known as
Tabulation( presenting data in the
form of rows and columns in a
Components of a table
Following are the principal
components of a table:-
first of all the table is to be
numbered. These numbers must be
in the same order as the tables.
Numbers facilitates the location of
the tables. For ex; table no. 1, 2, 3,
4, 5, 6, 7, 8, ........
a table must have a title. The title
must be written in bold letters. The
title must be simple, clear and short.
A good title must reveal:
i) The problem under consideration
ii) The time period of the study
iii)The place of study
iv)The nature of classification of data
“A GOOD TITLE IS SHORT BUT
COMPLETE IN ALL RESPECT”
If the title of the table does not give
complete information, it is
supplemented with head note.
Head note completes the
information in the title of the table.
The unit of data is preferably
expressed in lakhs, crores, tonnes
etc. and expressed in brackets as
stubs are the title of rows of a table.
These titles indicate information
contained in the rows of the table.
Caption is the title given to the
coloumns of a table. A caption
indicates information contained in
the coloumns of the table.
A caption may have sub-heads when
the information in the columns is
divided in more than one class.
body of a table means sum total of
the items in the table. Thus, body is
the most important part of the
table. It indicates values of the
various items in the table. Each
item in the body is called “Cell”
Footnotes are given for the
clarification of the reader. These
are generally given with
information in the table need to be
when table are based on secondary
data, source of the data is to be
given. Source of the data is
specified below the footnote.
Features of a good table
Construction of a table depends
upon the objective of study. It also
depends on the wisdom of
satisfaction. There are no hard and
fast rules for the construction of a
table. However, some important
guidelines should be kept in mind .
These are as under:-
1.) Title as compatible with objectives
of the study
Title of a table must be provided
at the top centre of the table and it
must be compatible with the
objectives of study.
Items which are to be compared
with each other should be placed in
rows and columns close to each
other. This facilitates comparison
3.) Special Emphasis
items in a table which needs
special emphesis should be placed
in head rows( top above ) or head
columns ( extreme left ). Such items
should be presented in Bold figures.
4.) Ideal size
Table must be of an ideal size, to
determine an ideal size. To
determine an ideal size of a table, a
rough draft or sketch must be
If the rows are long, stubs may be
given at right hand side of the
6.)Use of Zero
Zero should only be used to
indicate the quantity of the
variable. It should not be used to
indicate the non-availability of
data. If the data are not available
then it should be indicated by „n.a.‟
or ( - ) minus sign.
Heading should generally be
written in the singular form. For
ex., in the columns indicating
goods, the word “good” should be
Use of abbreviations should be
avoided in the heading or sub-
headings of a table.
Footnote should be given only if
Units may be specified above the
In the table, sub-totals of the items
must be given at the end of each
row. Grand total of the items must
also be noted.
12.) Percentage and Ratio
Percentage figures should be
provided in the table, if possible.
This makes the data more
13.) Extent of Approximation
If some approximate figures have
been used in the table, the extent of
approximation must be noted.
14.) Sources of Data
Sources of data must be noted at
the foot of the table. It is generally
noted next to the footnote.
15.) Size of columns
Size of columns must be uniform
16.) Ruling of columns
Columns must be divided into
different sections according to
similarities of the data.
17.) Simple, Economical and
a table must be simple attractive
and economical in space.
kinds of tables
A.) According to purpose
these tables are just for general purposes .
These tables are generally attached to some
official reports, like Census Reports of India.
These are also called Reference tables.
Specific purpose table is that table which is
prepared with some specific purpose in the
mind. In this table the data is presented in
the form of result of the analysis. That is why
these tables are also called Summary tables.
B.) According to Originality
An original table is that in which
data are presented in the same form
of the result of the analysis.
An derived table is that is that in
which data are not presented in the
form or manner in which these are
collected. Instead the data are
presented after converting data into
ratios and percentages.
C) Tables according to Construction
1) Simple or one-way
A simple table is that which shows
only one characteristics of the
CLASS No. of students
B.A. ( I ) 100
B.A.( II ) 80
B.A.( III ) 60
2) Complex Table
A complex table is one which
shows more than characteristic of
the data. On the basis of the
characteristics shown, these tables
may be further classified as:-
2.1) Double or two-way table
2.2) Treble table
2.3) Manifold table
2.1) Double or two-way table
A two way table is hat which shows two
characteristics of the data. e.x.,
No. of students
11th 160 40 200
B.A. ( I ) 40 60 100
B.A. ( II ) 60 20 80
B.A. ( III ) 50 10 60
tOTAL 310 130 440
2.2) Treble method
A table which shows three
characteristics of data. E.x.,
BOYS GIRLS TOTAL
11th 50 110 160 10 30 40 60 140 200
( I )
10 30 40 15 45 60 25 75 100
( II )
15 45 60 5 15 20 20 60 80
10 40 50 5 5 10 15 45 60
85 225 310 35 95 130 120 320 440
2.3) Manifold table
The manifold Table is he one that shows
more than three characteristics. E.x.,
boys girls tota
lrural urban rural urban
11th 5 55 10 90 2 8 5 25 200
( I )
5 15 15 35 4 4 4 18 100
( II )
5 10 15 30 2 3 5 10 80
5 5 20 20 3 2 2 3 60
20 85 60 175 11 17 16 56 440
Classification of data and
i) Qualitative classification
Qualitative data occours when the data are
classified on the basis of qualitative
characteristics for a phenomenon. E.x.,
Unemployement in punjab by
sex and location
sex rural Urban
Male 20 10
Female 30 20
Total 50 30
ii) Quantitative classification
In temporal classification data is
classified on the basis of quantitative
characteristics of a phenomenon. E.x.,
Marks obtained by students of
marks No. of students
A graph that uses rectangles (bars) to show numbers or
GLE 0406.5.1 SPI 0406.5.1
Parts of a bar graph.
Bar graphs are an excellent way to show results that happen
one time. It is an easy comparison tool for surveys, inventories,
and this type of data.
The bar graph is marked off with a series of lines called grid
Bar graphs can be horizontal or vertical. Both kinds will have
two axes. One axis gives the frequency information and the
other axis gives the group data.
Bar graphs must also have a title and labels on the axes.
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
Frequency of the data,
numbered in 10’s.
This axis gives the group data.
Histograms are bar graphs in which
• The bars have the same width and always touch (the
edges of the bars are on class boundaries which are
• The width of a bar represents a quantitative variable
x, such as age rather than a category.
• The height of each bar indicates frequency.
Before making a histogram, organize the data
into a frequency table which shows the
distribution of data into classes (intervals).
The classes are constructed so that each
data values falls into exactly one class, and
the class frequency is the number of data in
To find the class width,
First compute: Largest value - smallest Value
Desired number of classes
Increase the value computed to the next highest whole,
number even if the first value was a whole number. This
will ensure the classes cover the data.
The lower class limit of a class is the lowest data that can
fit into the class, the upper class limit is the highest data
value that can fit into the class. The class width is the
difference between lower class limits of adjacent classes.
Constructing Frequency Polygons
• Make a frequency table that includes class midpoints
• For each class place dots above class midpoint at the
height of the class frequency.
• Put dots on horizontal axis one class width to left of
first class midpoint, and one class width to right of of
• Connect dots with straight lines.
Cumulative Frequencies & Ogives
• The cumulative frequency of a class is the
frequency of the class plus the frequencies for
all previous classes.
• An ogive is a cumulative frequency polygon.
• Make a frequency table showing class boundaries
and cumulative frequencies.
• For each class, put a dot over the upper class
boundary at the height of the cumulative class
• Place dot on horizontal axis at the lower class
boundary of the first class.
• Connect the dots.
• Uniform (it has a rectangular histogram)
• Skewed left – the longer tail is on the left side.
• Skewed right – the longer tail is on the right side.
• Bimodal (the two classes with the largest
frequencies are separated by at least one class)