Editing Quantile (section)

==== Even-sized population ====

Consider an ordered population of 10 data values [3, 6, 7, 8, 8, 10, 13, 15, 16, 20]. What are the 4-quantiles (the "quartiles") of this dataset?

{| class="wikitable"
|-
! Quartile
! Calculation
! Result
|-
| Zeroth quartile
| Although not universally accepted, one can also speak of the zeroth quartile. This is the minimum value of the set, so the zeroth quartile in this example would be 3. 
| 3
|-
| First quartile
| The rank of the first quartile is 10&times;(1/4) = 2.5, which rounds up to 3, meaning that 3 is the rank in the population (from least to greatest values) at which approximately 1/4 of the values are less than the value of the first quartile. The third value in the population is 7.
| 7
|-
| Second quartile
| The rank of the second quartile (same as the median) is 10&times;(2/4) = 5, which is an integer, while the number of values (10) is an even number, so the average of both the fifth and sixth values is taken&mdash;that is (8+10)/2 = 9, though any value from 8 through to 10 could be taken to be the median.
| 9
|-
| Third quartile
| The rank of the third quartile is 10&times;(3/4) = 7.5, which rounds up to 8. The eighth value in the population is 15.
| 15
|-
| Fourth quartile
| Although not universally accepted, one can also speak of the fourth quartile. This is the maximum value of the set, so the fourth quartile in this example would be 20. Under the Nearest Rank definition of quantile, the rank of the fourth quartile is the rank of the biggest number, so the rank of the fourth quartile would be 10.
| 20
|}

So the first, second and third 4-quantiles (the "quartiles") of the dataset [3, 6, 7, 8, 8, 10, 13, 15, 16, 20]  are [7, 9, 15]. If also required, the zeroth quartile is 3 and the fourth quartile is 20.