CUMULATIVE FREQUENCY POLYGON or OGIVE

CUMULATIVE FREQUENCY POLYGON or OGIVE

1. Thegraphofacumulativefrequency
distributioniscalledaCUMULATIVE
FREQUENCY POLYGONorOGIVE.A
ogiveisobtainedbymarkingofftheupper
classboundariesofthevariousclasses
alongtheX-axisandthecumulative
frequenciesalongthey-axis,asshown
below:
CUMULATIVE
FREQUENCY POLYGON
or OGIVE

2. Example
The following table contains the ages
of 50 managers of child-care centers
in five cities of a developed country.
Construct the cumulative frequency
distribution and the cumulative
frequency polygon (ogive).

3. Ages of a sample of managers
of Urban child-care centers
42 26 32 34 57
30 58 37 50 30
53 40 30 47 49
50 40 32 31 40
52 28 23 35 25
30 36 32 26 50
55 30 58 64 52
49 33 43 46 32
61 31 30 40 60
74 37 29 43 54
Convert this data into Frequency Distribution.

4. Frequency Distribution of
Child-Care Managers Age
Class Limits Frequency
20 –29 6
30 –39 18
40 –49 11
50 –59 11
60 –69 3
70 –79 1
Total 50

5. Cumulative Frequency
The cumulative frequency is the
running total of the frequencies
through the total.
The cumulative frequency for each
class interval is the frequency for
that class interval added to the
preceding cumulative total.

6. Cumulative frequencies of child-
care data
Class
Limits
Frequency Cumulative
frequency
20 –29 6 6
30 –39 18 24
40 –49 11 35
50 –59 11 46
60 –69 3 49
70 –79 1 50
Total 50

7. Interpretation
24 of the 50 managers (i.e. 48% of
the managers) are 39 years of age
or less. (i.e. less than 40 years old.)
46 of 50 managers (i.e. 92% of the
managers) are 59 years of age or
less. (i.e. less than 60 years old.)
and so on.

8. Cumulative frequency polygon or
Ogive0
10
20
30
40
50
60
19.5 29.5 39.5 49.5 59.5 69.5 79.5

9. Example
Supposewewalkinthenursery
classofaschoolandwecounttheno.
ofBooksandcopiesthat45students
haveintheirbags.
Supposetheno.ofbooksandcopiesare
9,9,3,5,4,7,6,7,5,6,5,5,8,7,5,5,6,6,6,9,6,
7,6,6,4,5,5,6,6,6,6,7,7,8,5,8,8,7,9,
9,7,8,7,7,9,.

10. Representation of Data in a
Discrete Frequency Distribution
X Tally Frequency
3 | 1
4 ||| 3
5 |||| |||| 9
6 |||| |||| ||| 13
7 |||| |||| 10
8 ||| 3
9 |||| | 6
Total 45

11. Graphical Representation of
Discrete Data
8
10
12
2
4
6
0
X
14
No. of books and copies
No. of students

12. Relative Frequency Distribution
X Frequency Relative/ %
Frequency
3 1
1/45 x 100 = 2.22%
4 3
3/45 x 100 = 6.67%
5 9
9/45 x 100 = 20%
6 13
13/45 x 100 = 28.89%
7 10
10/45 x 100 = 22.22%
8 3
3/45 x 100 = 6.67%
9 6
6/45 x 100 = 13.33%
Total 45

13. Cumulative Frequency Distribution
X Frequency Cumulative
Frequency
3 1
1
4 3
1+3 = 4
5 9
4+9 = 13
6 13
13+13 = 26
7 10
26+10 = 36
8 3
36+3 = 39
9 6
39+6 = 45
Total 45