Percentile

There is no universally accepted definition of a percentile. Using the 65th percentile as an example, some statisticians define the 65th percentile as the lowest score that is larger than 65% of the scores. Others have defined the 65th percentile as the smallest score that is greater than or equal to 65% of the scores. A more sophisticated definition is given below.

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

R = P/100 x (N + 1)

where P is the desired percentile and N is the number of numbers. If R is an integer, then the Pth perentile is the number with rank R. When R is not an integer, we compute the Pth perentile by interpolation as follows:

1. Define IR as the integer portion of R (the numer to the left of the decimal point).
   
   
2. Define FR as the fractional portion or R.
   
   
3. Find the scores with Rank IR and with Rank IR + 1.
   
   
4. Interpolate by multiplying the difference between the scores by FR and add the result to the lower score.