graphical representation 2

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 24

2. RECAP
• Graphical Representation, Meaning, Graph V/S
Diagrams, General Rules of Graph

3. LEARNING OBJECTIVES
• After Studying this unit, the students able to know
how to present data Graphically using Histogram,
Frequency Polygon and Curve, and Pie charts and
working out cumulative frequency

4. LEARNING OUTCOMES
• Students will be able to analyze and interpret with
in the Contexts they are written in Diagrams and to
present data Graphically using Histogram,
Frequency Polygon and Curve, and Pie charts

5. SESSION - 23
• Construction of Graphs ( Histogram, Frequency
Polygon and Curve) Problems---------------01

6. Construction of Graphs
• Types of Graphs
Histogram
Frequency polygon
Frequency curve
Ogives or Cumulative frequency curve
HISTOGRAM;
A histogram is an attached bar chart or graph displaying
the distribution of a frequency distribution in visual
form. Take classes along the X-axis and the frequencies
along the Y-axis. Corresponding to each class interval, a
vertical bar is drawn whose height is proportional to the
class frequency.

7. CONTD
We cannot construct a histogram for distribution with
open-ended classes. The histogram is also quite
misleading, if the distribution has unequal intervals.
PROBLEM 01
The following table shows the time taken (in minutes)
by 100 students to travel to school on a particular day.
Draw Histogram.

8. CONTD

9. CONTD
• FREQUENCY POLYGON
Frequency polygon is drawn after drawing histogram for
a given frequency distribution. The area covered under
the polygon is equal to the area of the histogram.
Vertices of the polygon represent the class frequencies.
Frequency polygon helps to determine the classes with
higher frequencies.
PROBLEM 02. A firm reported that its Net Worth in the
years 2011-2016 are as follows. Draw frequency polygon

10. CONTD

11. CONTD
• FREQUENCY CURVE
Frequency curve is a smooth and free-hand curve drawn
to represent a frequency distribution. Frequency curve
is drawn by smoothing the vertices of the frequency
polygon.
Frequency curve provides better understanding about
the properties of the data than frequency polygon and
histogram.

12. CONTD
PROBLEM 03
The ages of group of pensioners are given in the table
below.
Draw the Frequency curve to the following data.

13. CONTD

14. SUMMARY
As we already discussed and learnt today on
Diagrammatic and Graphical Representation as below
• Construction of Graphs ( Histogram, Frequency
Polygon and Curve) Problems---------------01

15. MCQs
1 . Histogram can be drawn only for:
(a) Discrete frequency distribution
(b) Continuous frequency distribution
(c) Cumulative frequency distribution
(d) Relative frequency distribution
2. Histogram is a graph of:
(a) Frequency distribution
(b) Time series
(c) Qualitative data
(d) Ogive

16. MCQs
3 . When successive mid-points in a histogram are
connected by straight lines, the graph is called a:
(a) Histogram
(b) Ogive
(c) Frequency curve
(d) Frequency polygon
4. A frequency polygon is a closed figure which is:
(a) One sided
(b) Two sided
(c) Three sided
(d) Many sided

17. MCQs
5 . Frequency polygon can be drawn with the help of:
(a) Historigram
(b) Histogram
(c) Circle
(d) Percentage

18. CONTD
ANSWERS
1. B
2. A
3. D
4. D
5. B

19. REFERENCES
• S.P. Gupta, Sultan Chand and Sons Publications, 2017
• S. C. Gupta, Himalaya Publishing House,
Fundamentals of Statistics, 2018
• R.S.N Pillai and Bagavathi, S.Chand publications, 2010

20. THANK YOU