A Graph is Used to show the variations in a variable by means of a curve or a straight.
Persons seeing graphs have not to bother themselves about the figures.
Utility Of Graphic Presentation
(1)Presentation Of Time Series and Frequency Distribution : Graphic Presentation is a
very effective technique of data presentation in case of time series and frequency
(2)Location of Averages: Using graphic technique, we can easily locate the value of
certain averages, such as mode and median. If it is not possible with help of diagram
(3)Easy Estimation : Graphic presentation facilitates interpolation and extrapolation of
the data in a more convenient and precise manner. For example, given population
data for the years 1951 and 1971, one can easily make an estimate of the population
in the years 1981 or 1991
(4) Study Of Correlation : Graphic technique helps in studying correlation between
different variables, such as price and demand, cost and output.
(5) Comparison Of Multiple-Dam: Data of different dimensions can be easily
compared with help of graphic presentation.
Limitations Of Graphic Presentation
(1) Less Significant : Graphs are not equal significance to all the
people. It is generally difficult for layman to interpret graphs
(2) Only a Measure Tendency : Graphs show only tendency of data.
Actual values are not always clear from graphs.
(3) Lack of precise Value: Since graphs are based on brief
information, these do not show precise values.
(4) Wrong Conclusion : Graphs may sometimes suggest wrong
conclusions. In fact even a small change in the scale of graphs
causes a lot of difference in structure of graph. This may lead to
Time Series Graphs
• A time series is an arrangement of statistical
data in a Chronological order. The Graph of
time series with time on X-axis and dependent
variable on Y-variable is called a historigrams.
• Time series analysis comprises methods for
analyzing time series data in order to extract
meaningful statistics and other characteristics
of the data
One Variable Graphs
One variable graphs are those graphs in which values of only one variable are
shown with respect to different time periods.
This table shows the net revenue earned by railways during nine Years
Net revenue for Indian Railways
Month Jan Feb Mar April May June
Production 7.5 10 7.5 12.5 15 17.5
Sale 5 7.5 5 10 12.5 15
Two or More than two variable graphs
Frequency Distribution Graphs are those graphs
which present the frequency distribution of data on
graph paper. These graphs are prepared to present
those data which are not related to any time period.
The data presented in these graphs are in the form
of frequency distribution,ethier grouped or
ungrouped. It quickly Calls attention to high to low
points in the distribution.
A line Frequency Graph is that which presents a
discrete frequency distribution of data on graph paper.
In such graph, various items of values are shown on X-
axis and their corresponding frequencies on Y-axis.
Frequency of the values are shown in the Form of
vertical straight lines.
45 50 55 60 65 70
Height In Inches
Line Frequency Graph
Height(in Inches) 45 50 55 60 65 70
No of Students 5 6 10 15 12 5
An Histogram Is a Graphical Representation of a
frequency of a frequency distribution of a
continuous series. It represents the class
frequencies in a frequency distribution by vertical
rectangles meeting each other from left to right.
The Total area covered under a histogram is
proportional to the total frequency.
When the class intervals are unequal, frequencies are first
adjusted before constructing a histogram. For making the
adjustment, we first determine the adjustment factor by using
the formula: Adjusted Factor=Size of class interval/lowest class
interval. Then we divide the frequencies by adjustment factor
and obtain the new adjusted frequency density, The height of the
rectangles would be proportional to the adjusted frequencies
There are two ways in which frequency polygon may
be constructed :
A graph of a frequency distribution with values of the
variable on the x-axis and the number of observations
on the y-axis; data points are plotted at the midpoints
of the intervals and are connected with a straight line.
A Frequency Curve is the smoothed form of
frequency polygon. A frequency curve is
obtained by joining the points of a frequency
polygon through free hand smoothed curves and
not through straight lines. Area of a frequency
curve is equal to the area of a frequency
10 5 15 25 35 45 55 60
Marks 0-10 10-20 20-30 30-40 40-50 50-60
No. of students 5 12 15 22 14 4
Mid values 5 15 25 35 45 55
An Ogive is the curve which is constructed by plotting
the cumulative frequencies in the form of smooth
curve. From such curves, We come to know about the
frequencies corresponding to a certain lower or
upper limits in the distribution of the data.
There are two methods of constructing an Ogive:
Marks No of students
Marks(less than) Cumulative Frequency
In this method, we start with the upper limits of the classes and go on
adding frequencies. When these frequencies are plotted, we get a rising
curve. The resultant curve is called “less than Ogive”.
0 10 20 30 40 50 60 70
Less than Ogive
Marks No of students
Marks(more than) Cumulative Frequency
In this method, we start with the lower limits of the classes and add
frequencies from the bottom. When the frequencies are plotted, we get a
declining curve. The resultant curve is called a “More than Ogive”
0 10 20 30 40 50 60 70
More than Ogive