**Presentation of Data- Geometric Diagram**

**DIAGRAMMATIC PRESENTATION OF DATA**

This is the third method of presenting
data. This method provides the
quickest understanding of the actual
situation to be explained by data in
comparison to tabular or textual
presentations.

Diagrammatic presentation of data translates quite effectively
the highly abstract ideas contained in numbers into more concrete and easily
comprehensible form.
Diagrams may be less accurate but
are much more effective than tables in
presenting the data.
There are various kinds of diagrams
in common use. Amongst them the
important ones are the following:

(i) Geometric diagram

(ii) Frequency diagram

(iii) Arithmetic line graph

**Geometric Diagram:-**

Bar diagram and pie diagram come in
the category of geometric diagram. The
bar diagrams are of three types — simple,
multiple and component bar diagrams.

**a)Bar Diagram**

Simple Bar Diagram
Bar diagram comprises a group of
equi spaced and equi width rectangular
bars for each class or category of data.
Height or length of the bar reads the
magnitude of data

**b)Multiple Bar Diagram**

Multiple bar diagrams are
used for comparing two or more sets of
data, for example income and
expenditure or import and export for different years, marks obtained in
different subjects in different classes,
etc.

**c)Component Bar Diagram**

Component bar diagrams or charts
(Fig.4.3), also called sub-diagrams, are
very useful in comparing the sizes of
different component parts (the elements
or parts which a thing is made up of)
and also for throwing light on the
relationship among these integral parts.

**d)Pie Diagram**

A pie diagram is also a component
diagram, but unlike a bar diagram,
here it is a circle whose area is
proportionally divided among the
components (Fig.4.4) it represents. It
is also called a pie chart. The circle is
divided into as many parts as there are
components by drawing straight lines
from the center to the circumference.
Pie charts usually are not drawn
with absolute values of a category.

Pie charts usually are not drawn
with absolute values of a category. The
values of each category are first
expressed as percentage of the total
value of all the categories. A circle in a
pie chart, irrespective of its value of
radius, is thought of having 100 equal
parts of 3.6° (360°/100) each. To find
out the angle, the component shall
subtend at the center of the circle, each
percentage figure of every component
is multiplied by 3.6°. An example of this
conversion of percentages of
components into angular components
of the circle is shown below.

**Frequency Diagram**

Data in the form of grouped frequency
distributions are generally represented
by frequency diagrams like histogram,
frequency polygon, frequency curve
and ogive.

**Histogram**

A histogram is a two dimensional
diagram. It is a set of rectangles with
base as the intervals between class
boundaries (along X-axis) and with
areas proportional to the class
frequency . If the class intervals
are of equal width, which they generally
are, the area of the rectangles are
proportional to their respective
frequencies. However, in some type of
data, it is convenient, at times
necessary, to use varying width of class
intervals.

When bases vary in their width, the
heights of rectangles are to be adjusted
to yield comparable measurements.
The answer in such a situation is
frequency density (class frequency
divided by width of the class interval)
instead of absolute frequency.

**Frequency Polygon**

A frequency polygon is a plane
bounded by straight lines, usually four
or more lines. Frequency polygon is an
alternative to histogram and is also
derived from histogram itself.

Statistics deals with the collection of data and information for a particular purpose. The tabulation of each run for each ball in cricket gives the statistics of the game. Tables, graphs, pie-charts, bar graphs, histograms, polygons etc .are used to represent statistical data pictorially.

Frequency polygon can be fitted to a
histogram for studying the shape of the
curve. The simplest method of drawing
a frequency polygon is to join the
midpoints of the topside of the
consecutive rectangles of the
histogram. A frequency polygon is almost identical to a histogram, which is used to compare sets of data or to display a cumulative frequency distribution. It uses a line graph to represent quantitative data.

**Ogive**

Ogive is also called cumulative
frequency curve. As there are two types
of cumulative frequencies, for example
‘‘less than’’ type and ‘‘more than’’ type,
accordingly there are two ogives for any
grouped frequency distribution data.
Here in place of simple frequencies as
in the case of frequency polygon,
cumulative frequencies are plotted
along y-axis against class limits of the
frequency distribution.

For ‘‘less than’’
ogive the cumulative frequencies are
plotted against the respective upper
limits of the class intervals whereas for
more than ogives the cumulative
frequencies are plotted against the
respective lower limits of the class
interval. An interesting feature of the
two ogives together is that their
intersection point gives the median. As
the shapes of the two ogives suggest,
‘‘less than’’ ogive is never decreasing
and ‘‘more than’’ ogive is never
increasing.

**Arithmetic Line Graph**

An arithmetic line graph is also called
time series graph. In this graph, time (hour, day/date, week, month,
year, etc.) is plotted along x-axis and
the value of the variable (time series
data) along y-axis.

A line graph
by joining these plotted points, Frequency distribution of marks
obtained in mathematics
thus, obtained is called arithmetic
line graph (time series graph). It
helps in understanding the trend,
periodicity, etc., in a long term time
series data.

Example: