Editing Quantile (section)

==== Odd-sized population ====

Consider an ordered population of 11 data values [3, 6, 7, 8, 8, 9, 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 first quartile is determined by 11&times;(1/4) = 2.75, 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 second quartile value (same as the median) is determined by 11&times;(2/4) = 5.5, which rounds up to 6. Therefore, 6 is the rank in the population (from least to greatest values) at which approximately 2/4 of the values are less than the value of the second quartile (or median). The sixth value in the population is 9.
| 9
|-
| Third quartile
| The third quartile value for the original example above is determined by 11&times;(3/4) = 8.25, which rounds up to 9. The ninth 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 11.
| 20
|}

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