graphical representation 4

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 26

2. RECAP
• Construction of Graphs ( Histogram, Frequency
Polygon and Curve) Problems--------------- 02

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 - 26
• Construction of Graphs ( Less than Ogive or
Cumulative Frequency) Problems---------------02

6. Cumulative Frequencies Curve or Ogives
MEANING
• Cumulative frequency curve (Ogive) is drawn to
represent the cumulative frequency distribution. There
are two types of Ogives such as ‘less than Ogive curve’
and ‘more than Ogive curve’. To draw these curves, we
have to calculate the ‘less than’ cumulative
frequencies and ‘more than’ cumulative frequencies.
The following procedure can be followed to draw the
ogive curves:
• Less than Ogive: Less than cumulative frequency of
each class is marked against the corresponding upper
limit of the respective class. All the points are joined by
a free-hand curve to draw the less than ogive curve.

7. CONTD
• More than Ogive: More than cumulative frequency of
each class is marked against the corresponding lower
limit of the respective class. All the points are joined
by a free-hand curve to draw the more than
ogive curve.
• Both the curves can be drawn separately or in the
same graph. If both the curves are drawn in the same
graph, then the value of abscissa (x-coordinate) in the
point of intersection is the median.

8. CONTD
PROBLEM 01
Draw the less than Ogive curve for the following data:

9. CONTD
Solution;
The less than cumulative frequency of Number of
workers are plotted as points against the daily wages
(upper-limit). These points are joined to form less
than ogive curve.

10. CONTD

11. CONTD
PROBLEM 02
The ages of group of pensioners are given in the table
below.
Draw the Less than ogive to the following data.

12. CONTD
SOLUTION;
Age
No of
Pensioners CF
65-70 38 38
70-75 45 83
75-80 24 107
80-85 10 117
85-90 8 125

13. CONTD
0
20
40
60
80
100
120
140
70 75 80 85 90
CUMULATIVE FREQUENCIES

14. SUMMARY
As we already discussed and learnt today on
Diagrammatic and Graphical Representation as below
• Construction of Graphs ( Less than Ogive or
Cumulative Frequency) Problems---------------02

15. MCQs
1 . Ogive curve can be occurred for the distribution of:
(a) Less than type
(b) More than type
(c) Both (a) and (b)
(d) Neither (a) and (b)
2 . The word ogive is also used for:
(a) Frequency polygon
(b) Cumulative frequency polygon
(c) Frequency curve
(d) Histogram

16. MCQs
3 . Cumulative frequency polygon can be used for the
calculation of:
(a) Mean
(b) Median
(c) Mode
(d) Geometric mean
4. The graph of the cumulative frequency distribution is
called:
(a) Histogram
(b) Frequency polygon
(c) Pictogram
(d) Ogive

17. MCQs
5 . In a cumulative frequency polygon, the cumulative
frequency of each class is plotted against:
(a) Mid-point
(b) Lower class boundary
(c) Upper class boundary
(d) Upper class limit

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

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