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.
P_{50} 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 , in the table of cumulative frequency.
L_{i} is the lower limit of the percentile class.
N is the sum of the absolute frequency.
F_{i-1} is the absolute frequency immediately below the percentile class.
a_{i} 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:
f_{i} | F_{i} | |
---|---|---|
[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 |