Less Than Cummulative Frequecy Distribution
Less Than Cumulative Frequency Table
-Cumulative frequency curve or an ogive is the graphical representation of a cumulative frequency distribution. There are two methods of constructing an ogive
(i) Less than method (ii) More than method
(i) Less than method : - Following are the steps for construction of an ogive :
(a) Construct a cumulative frequency table of less than type.
(b) Mark upper class limits along X-axis.
(c) Mark the corresponding cumulative frequency along Y-axis.
(d) Plot the points where
is the upper limit of a class and
is the corresponding c.f. and join them by a smooth free hand curve.
The curve we get is the Less Than Type Ogive.
Illustration : - Draw an ogive for the following frequency distribution by less than method.
| Class Interval | 0-8 | 8-16 | 16-24 | 24-32 | 32-40 | 40-48 |
|---|---|---|---|---|---|---|
| Frequency | 8 | 12 | 20 | 16 | 8 | 10 |
Solution : First we prepare a Less Than Type frequency distribution table.
| Class Interval | Cumulative Frequency |
|---|---|
| Less than 8 | 8 |
| Less than 16 | 8+12=20 |
| Less than 24 | 20+20=40 |
| Less than 32 | 40+16=56 |
| Less than 40 | 56+8=64 |
| Less than 48 | 64+10=74 |
Now, mark the upper class limit on X-axis and frequency along Y-axis, plot the point (8,8), (16,20), (24,40), (32,56), (40,64) and (48,74). Join the points by smooth free hand curve to get required less than type ogive.
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