4) Ogives or Cumulative Frequency Curves:-
When frequencies are added, they are called cumulative frequencies.
The curve obtained by plotting cumulating frequencies is called
a cumulative frequency curve or an ogive ( pronounced ojive ).
To construct an Ogive:-
1) Add up the progressive totals of frequencies, class by
class, to get the cumulative frequencies.
2) Plot classes on the horizontal ( x-axis ) and cumulative
frequencies on the vertical ( y-axis).
3) Join the points by a smooth curve. Note that Ogives start
at (i) zero on the vertical axis, and (ii) outside class limit
of the last class. In most of the cases it looks like 'S'.
Note that cumulative frequencies are plotted against the
'limits' of the classes to which they refer.
(A) Less than Ogive:- To plot a less than ogive, the data is arranged in ascending order of magnitude and the frequencies are cumulated starting from the top. It starts from zero on the y-axis and the lower limit of the lowest class interval on the x-axis.
(B) Greater than Ogive:- To plot this ogive, the data are arranged in the ascending order of magnitude and frequencies are cumulated from the bottom. This curve ends at zero on the the y-axis and the upper limit of the highest class interval on the x-axis.
Illustrations:- On a graph paper, draw the
two ogives for the data given below of the I.Q. of 160 students.
Class -intervals :60 - 70 70 - 80 80 - 90 90 - 100 100 - 110
No. of students : 2 7 12 28 42
110 - 120 120 - 130 130 - 140 140 - 150 150 - 160
36 18 10 4 1