As it has been already mentioned the positional averages viz. Median, Quartiles, Deciles, Percentiles etc. can be determined by graphic method also, However, the method is suitable only for the continuous series for which only, it is possible to draw either a Less than, or a More than O give curve:
The following steps are to be taken in turn for determining Median etc. through a less than ogive curve:
- Arrange the value column in “Less than” order along with their corresponding cumulative frequencies in an ascending order.
- Draw the first quadrant of a graph taking both the horizontal, and vertical axes in the positive direction.
- Arrange the less than values along the horizontal axis by putting the different upper limits at the proportionate distance.
- Arrange the frequencies along the vertical axis on a natural scale so as to accommodate the maximum cumulative frequency on it.
- Plot the different points of intersection of the values, and their respective cumulative frequencies on the graph paper and then draw the curve in a freehand manner. Such a curve is called “Less than ogive”
- Compute the required items of the Median, Quartile, Declie, Percentile etc. with their respective basis formula viz. N/2, N/4, N/10 or N/100 as the case may be.
- With reference to the required item thus computed, draw a perpendicular from the vertical axis on the ogive curve, and then form the point touching the ogive curve, draw another perpendicular to the horizontal axis. The point thus located on the horizontal axis will indicate the value of the relevant item viz. Median, Quartile, Declie or Precentile.
On the other hand, if it is required to ascertain the number of the item i.e. frequency for any particular value of a variable, the same may be determined through the ogive curve by drawing as perpendicular from the point of the ogive to the vertical axis. The point of frequency at which such a perpendicular touches indicates the required number of item.