Percentiles and percentile rank
Just like quartiles, percentiles and percentile rank are among the measures of position. Percentiles divide a ranked data (ordered set of data ) into 100 equal parts. 99 percentiles are needed to divide any data set into 100 equal parts.
The data should be ranked in increasing order to compute percentiles.
The kth percentile is denoted by Pk where k is an integer from 1 to 99
just like the first quartile is denoted by Q1
First percentile is denoted by P1
Second percentile is denoted by P2
And so forth…
Do you recall the meaning of the first quartile or Q1 ?
It means that 25% of the values are less than Q1. By the same token,
First percentile means that 1% of the values are less than P1 or 99% of the values are bigger than P1
In general, the kth percentile , Pk , can be defined as a value in a data set such that about k% of the values are smaller than the value of Pk and about (100 – k)% of the values are bigger than the value of Pk
Percentiles and percentile rank formulas
The value of the kth percentile is Pk = the value of the ( kn /100 )th term in a ranked data set
k is the number of the perpentile and n is the sample size.
Percentile rank of a value
Percentile rank of xi = (Number of values less than xi / Total number of values in the data set ) × 100