Percentiles and Quartiles


Percentiles

A percentile is a measure at which that percentage of the total values are the same as or below that measure. For example, 90% of the data values lie below the 90th percentile, whereas 10% of the data values lie below the 10th percentile.

Quartiles

Quartiles are values that divide a (part of a) data table into four groups containing an approximately equal number of observations. The total of 100% is split into four equal parts: 25%, 50%, 75% and 100%.

The first quartile (or lower quartile), Q1, is defined as the value that has an f-value equal to 0.25. This is the same thing as the twenty-fifth percentile. The third quartile (or upper quartile), Q3, has an f-value equal to 0.75. The interquartile range, IQR, is defined as Q3-Q1.

The percentiles and quartiles are computed as follows:

  1. The f-value of each value in the data table is computed:
      
    where i is the index of the value, and n the number of values.

  2. The first quartile is computed by interpolating between the f-values immediately below and above 0.25, to arrive at the value corresponding to the f-value 0.25.

  3. The third quartile is computed by interpolating between the f-values immediately below and above 0.75, to arrive at the value corresponding to the f-value 0.75.

  4. Any other percentile is similarly calculated by interpolating between the appropriate values.

Example:

Value

f-value

4

0

8

0.2

9

0.4

11

0.6

16

0.8

17

1.0

Interpolation at f-value=0.75 yields Q3=14.75.

See also:

Adjacent Values and Outliers

Aggregations Overview