Percentiles and Quartiles
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 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 f-value of each value in
the data table is computed:
where
is the index of the value,
and
n he number of values.
- 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.
- 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.
- 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.
