Percentile (Statistics)

Define percentile:

Instead of dividing the total frequency into 4 parts by quartiles, we may divide it into 100 parts by what are called percentiles. Or we may divide into 10 parts by decile. The theory of percentiles is precisely analogous to that of the quartiles. Like the quartiles, there may, for instance, be certain indeterminacies in their exact percentile definition which are removed by supplementary conventions. Percentiles can be obtained by arithmetical or graphical interpolation. Percentiles have obvious meanings.

These quantities such as quartiles, deciles and percentiles, which divide the total frequency into a number of parts, are called quantiles or grades, and when we speak of the grade of an individual we mean thereby the proportion of the total frequency which lies below it. For example, when we say that a student has scored 75 percentile, we mean that of the total number of students who have appeared for the test, 75% of them have scored below this student.

Finding the percentile:

The percentile can be conveniently found by a graphical method which is an extension  of the graphical method of finding the median. Against the variate value as abscissa we graph as ordinate the cumulated frequency up to and including the corresponding variate value. This is called the distribution curve. By reading off the ordinate corresponding to a given variate we can find the number of members of the population bearing that or lower value. Similarly, by reading off the variate corresponding to the given ordinate we can find the percentiles.

A somewhat similar form of graph (with the percentiles as abscissa and the variate a ordinate) was formerly in use and was known as Galton’s ogive. The curve was not, however, always shaped like an ogive. The distribution curve appears to provide a more natural method of representation and a better name. We recognize it as the graph of the integral of the frequency curve.

Percentile uses:

In statistics percentile has been found to be very useful when dealing with non measurable characters. For example, the capacity of different boys in a class as regards some school subject cannot be directly measured, but it may not be very difficult for the teacher to arrange them in order of merit as regards this particular character. If the boys are then numbered up in that order, the number of each boy, or his rank, becomes more or less his representative of his percentile. So the third ranker in a group of 50 boys would be the 94th percentile and so on.