Percentiles

The percentiles are the 99 values of the variable that divide an ordered data set into 100 equal parts.

The percentiles determine the values for 1%, 2%... and 99% of the data.

P50 coincides with the median.

Calculating Percentiles

1. Order the data from smallest to largest.

2. Look for the place that occupies every percentile by means of the expression Percentile Expression, in the table of cumulative frequency.

Percentile Formula

Li is the lower limit of the percentile class.

N is the sum of the absolute frequency.

Fi-1 is the absolute frequency immediately below the percentile class.

ai is the width of the class containing the percentile class.

The percentiles are independent of the widths of the classes.


Example

Calculate the percentiles of the distribution for the following table:

  fi Fi
[50, 60) 8 8
[60, 70) 10 18
[70, 80) 16 34
[80, 90) 14 48
[90, 100) 10 58
[100, 110) 5 63
[110, 120) 2 65
  65  

Percentile 35

Calculating the 35th Percentile

Percentile Calculation

Percentile 60

Calculating the 60th Percentile

Percentile Calculation