Concept of Ogive- For drawing less than cumulative frequency polygon or curve (or less than ogive), first of all the cumulative frequencies are plotted against the values (upper limits of the class intervals) up to which they correspond and then we simply join the points by line segments, curve thus obtained is known as less than ogive. Similarly, more than frequency curve (more than ogive) can be obtained by plotting more than cumulative frequencies against lower limits of the class intervals. As we have already mentioned within brackets that less than cumulative frequency curve and more than cumulative frequency curve are also called less than ogive and more than ogive respectively.
We can define as follows-
Less Than Ogive
If we plot the points with the upper limits of the classes as abscissae and the cumulative frequencies corresponding to the values less then the upper limits as ordinates and join the points so plotted by line segments, the curve thus obtained is nothing but known as “less than cumulative frequency curve” or “less than ogive”.
More Than Ogive
If we plot the points with the lower limits of the classes as abscissa and the cumulative frequencies corresponding to the values more than the lower limits as ordinates and join the points so plotted by line segments, the curve thus obtained is nothing but known as “more than cumulative frequency curve” or “more than Ogive”.
Note-
Median may also the obtained by drawing dotted vertical line through the point of inter section of both the ogives, when drawn on a single figure.
Example
Draw less than type and more than type ogive of the following data-
| Weekly wages | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| workers | 45 | 55 | 70 | 40 | 10 |
Sol:
We prepare the table for both less than type and more than type:
| Weekly wages | Workers | Less than cumulativeWages less than workers | more than cumulativeWages more than workers |
| 0-10 | 45 | 10 45 | 0 220 |
| 10-20 | 55 | 20 100 | 10 175 |
| 20-30 | 70 | 30 170 | 20 120 |
| 30-40 | 40 | 40 210 | 30 50 |
| 40-50 | 10 | 50 220 | 40 10 |
From above data, we construct both the ogives as shown in Figure below
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