Ogive

These are cumulative frequency graphs drawn on a natural scale to determine the values of certain factors viz. Median, Quartiles, Deciles, Percentiles etc. In these graphs, the class limits are shown along the X-axis, and the cumulative frequencies are shown along the Y-axis. Since the class limits along with their frequencies can be arranged in two different orders viz. (i) Less than order, and frequencies can be arranged in two different orders viz. (i) Less than order, and (ii) More than order, there can be two types of ogives, i.e. (i) Less than order, and (ii) More than order, there can be two types of ogives, i.e. (i) Less than ogive and (ii) More than ogive. The technique of drawing these two types of ogives are detailed here as under:

(i) Less than Ogive:

For drawal of a less than ogive the following steps are to be taken up in turn:

1. The given series is to be converted into the less than form (if not in this form already) in an ascending order by starting with the upper limit of the lowest class.

2. The corresponding frequencies are to be cumulated gradually, giving rise to an ascending order as well.

3. The X-axis is to represent all the upper limits beginning with the minimum upper limit at the point of origin.

4. The Y-axis is to represent the cumulative frequencies beginning with zero at the base.

5. The dots should be put at each of the coordinating points of the upper limit and the corresponding frequencies.

6. Lastly, a line is to be drawn smoothly joining all the dots thus put. This would give rise to a curve which is to be designated as the ‘Less than Ogive’.

(ii) More than Ogive:

For drawal of a more than ogive, the following steps already) in an ascending order by starting with the lower limit of the lowest class.

1. Convert the given series in to the ‘more than’ form (if not in this form already) in an ascending order by starting with the lower limit of the lowest class.

2. Put the cumulative frequencies against the corresponding lower limits carefully showing them in a descending order.

3. Represent all he lower limits along the X-axis beginning with the minimum of the lower limits at the point of origin.

4. Represent the cumulative frequencies along the Y-axis beginning with zero at the point of origin.

5. Put the dots at each of the coordinating points and join them all by a smoothly drawn line.

6. Designate the curve so drawn as the ‘More than’ ogive.