Page:Online Statistics Education.pdf/30

 A Third Definition

Unless otherwise specified, when we refer to “percentile,” we will be referring to this third definition of percentiles. Let's begin with an example. Consider the 25th percentile for the 8 numbers in Table 1. Notice the numbers are given ranks ranging from 1 for the lowest number to 8 for the highest number.

Table 1. Test Scores.

The first step is to compute the rank (R) of the 25th percentile. This is done using the following formula:

$$R=\frac{P}{100}\times(N+1)$$

where P is the desired percentile (25 in this case) and N is the number of numbers (8 in this case). Therefore,

$$R=\frac{25}{100}\times(8+1)=\frac{9}{4}=2.25$$

If R is an integer, the Pth percentile is be the number with rank R. When R is not an integer, we compute the Pth percentile by interpolation as follows:

1. Define IR as the integer portion of R (the number to the left of the decimal point). For this example, IR=2.

2. Define FR as the fractional portion of R. For this example, FR=0.25. 30