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 Pwhere k is an integer from 1 to 99

Just like the first quartile is denoted by Q1, the 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 , P, can be defined as a value in a data set such that about k% of the values are smaller than the value of Pand about (100 - k)% of the values are bigger than the value of Pk

Percentiles and percentile rank formulas

Percentiles

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 percentile 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

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