PERCENTILE_CONT and MEDIAN

PERCENTILE_CONT is an inverse distribution function. It assumes a continuous distribution between values of the expression in the sort specification. Then, it interpolates the value of that expression at the given percentile, performing a linear interpolation. For an overview of window functions in SingleStore, see Window Functions Guide.

Syntax

PERCENTILE_CONT(percentile)
WITHIN GROUP (ORDER BY (col | expr))
[OVER (
    [PARTITION BY (col | expr), ...]
    [frame_clause]
)]

or equivalently

PERCENTILE_CONT(percentile)
OVER (
        ORDER BY (col | expr)
        [PARTITION BY {col | expr}, ...]
        [frame_clause]
)

Also, MEDIAN can be used as a regular aggregate function, as follows:

MEDIAN (col | expr)

Arguments

percentile

A numeric value between 0 and 1.

col

A column of a numeric data type.

expr

An expression that evaluates to a numeric data type.

Remarks

Both the PERCENTILE_CONT and MEDIAN functions can be used as standard aggregate functions.

The OVER() clause defines how to partition the input set. If no PARTITION BY clause is specified, the entire input set is treated as a single partition.

Only one column or expression is allowed in the ORDER BY clause, and this column is the one for which the percentile is calculated.

Examples

Example 1

The following example demonstrates the use of PERCENTILE_CONT as an aggregate function.

SQL

CREATE TABLE percont_sets (a INT, b INT, c INT);

INSERT INTO percont_sets VALUES (1,1,2),(2,2,3),(3,1,2),(4,2,4),(5,1,1),(2,1,1),(null,null,3);

SQL

SELECT PERCENTILE_CONT(0.5)
WITHIN GROUP (ORDER BY a)
FROM percont_sets;

+------------------------------------------------+
| PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY a) |
+------------------------------------------------+
|                                         2.5000 |
+------------------------------------------------+

SQL

SELECT c, PERCENTILE_CONT(0.5)
WITHIN GROUP (ORDER BY a) AS "PERCENTILE"
FROM percont_sets
GROUP BY c ORDER BY c;

+------+------------+
| c    | PERCENTILE |
+------+------------+
|    1 |     3.5000 |
|    2 |     2.0000 |
|    3 |     2.0000 |
|    4 |     4.0000 |
+------+------------+

SQL

SELECT PERCENTILE_CONT(0.25)
WITHIN GROUP (ORDER BY a) AS "PERCENTILE"
FROM percont_sets;

+------------+
| PERCENTILE |
+------------+
|     2.0000 |
+------------+

The percentile of a data set may change depending on how it is ordered.

SQL

SELECT PERCENTILE_CONT(0.25)
WITHIN GROUP (ORDER BY a DESC) AS "PERCENTILE"
FROM percont_sets;

+------------+
| PERCENTILE |
+------------+
|     3.7500 |
+------------+

Multiple PERCENTILE_CONT functions can be used in a single query, and each function must have its own WITHIN GROUP clause.

SQL

SELECT PERCENTILE_CONT(0.25)
      WITHIN GROUP (ORDER BY a) AS "PERCENTILE a",
      PERCENTILE_CONT(0.25)
      WITHIN GROUP (ORDER BY b) AS "PERCENTILE b"
FROM percont_sets;

+--------------+--------------+
| PERCENTILE a | PERCENTILE b |
+--------------+--------------+
|       2.0000 |       1.0000 |
+--------------+--------------+

Example 2

The following example creates a table containing SAT scores. The resulting window frame shows the hypothetical 90th percentile SAT score given the existing scores.

SQL

CREATE TABLE percont_SAT (reading_writing int, math int);

INSERT INTO percont_SAT VALUES (800,800),(650,300),(700,500);

SQL

SELECT reading_writing, math, reading_writing + math AS total,
PERCENTILE_CONT(.9)
WITHIN GROUP (ORDER BY reading_writing + math)
OVER () AS `90th Percentile`
FROM percont_SAT;

+-----------------+------+-------+-----------------+
| reading_writing | math | total | 90th Percentile |
+-----------------+------+-------+-----------------+
|             650 |  300 |   950 |       1520.0000 |
|             700 |  500 |  1200 |       1520.0000 |
|             800 |  800 |  1600 |       1520.0000 |
+-----------------+------+-------+-----------------+

Median

Compute the median using percentile = 0.5.

PERCENTILE_CONT( 0.5 ) ...

Example:

SQL

CREATE TABLE percont (a int);

INSERT INTO percont VALUES (1),(2),(3),(166),(1024);

SQL

SELECT a, AVG(a) OVER () AS mean,
PERCENTILE_CONT(.5)
WITHIN GROUP (ORDER BY a)
OVER () AS median
FROM percont;

+------+----------+--------+
| a    | mean     | median |
+------+----------+--------+
|    1 | 239.2000 | 3.0000 |
|    2 | 239.2000 | 3.0000 |
|    3 | 239.2000 | 3.0000 |
|  166 | 239.2000 | 3.0000 |
| 1024 | 239.2000 | 3.0000 |
+------+----------+--------+

Median and Percentiles with Regular Aggregates and Grouping

Suppose you have some data with columns you want to group by and another column you want to aggregate using several aggregate functions, including standard ones like AVG, MIN, MAX etc., as well as percentiles and median. In other words, you want to use percentile functions and median just like regular aggregates.

For example, suppose you have the following data:

SQL

CREATE TABLE percont_t (id int, category varchar(10), year int, value int);
INSERT INTO percont_t VALUES
  (1, "ABC", 2019, 100),
  (2, "ABC", 2019, 150),
  (3, "ABC", 2019, 200),
  (4, "ABC", 2020, 100),
  (5, "ABC", 2020, 175),
  (6, "ABC", 2020, 250),
  (7, "XYZ", 2020, 200),
  (8, "XYZ", 2020, 275),
  (9, "XYZ", 2020, 350),
  (10, "XYZ", 2020, 450);

Suppose you want to compute the following aggregates of value grouped by category and year for this data: SUM, AVG, MEDIAN, 10th percentile, and 90th percentile. The query you specify is:

SQL

SELECT category, year, SUM(value), AVG(value), MEDIAN(value),
  PERCENTILE_CONT(0.1) WITHIN GROUP (ORDER BY value),
  PERCENTILE_CONT(0.9) WITHIN GROUP (ORDER BY value)
FROM percont_t
GROUP BY category, year
ORDER BY category, year;

+----------+------+------------+------------+---------------+----------------------------------------------------+----------------------------------------------------+
| category | year | SUM(value) | AVG(value) | MEDIAN(value) | PERCENTILE_CONT(0.1) WITHIN GROUP (ORDER BY value) | PERCENTILE_CONT(0.9) WITHIN GROUP (ORDER BY value) |
+----------+------+------------+------------+---------------+----------------------------------------------------+----------------------------------------------------+
| ABC      | 2019 |        450 |   150.0000 |      150.0000 |                                           110.0000 |                                           190.0000 |
| ABC      | 2020 |        525 |   175.0000 |      175.0000 |                                           115.0000 |                                           235.0000 |
| XYZ      | 2020 |       1275 |   318.7500 |      312.5000 |                                           222.5000 |                                           420.0000 |
+----------+------+------------+------------+---------------+----------------------------------------------------+----------------------------------------------------+

The above query gives the desired result because both the PERCENTILE_CONT and MEDIAN functions are allowed as standard aggregate functions. Also, it’s not necessary to use window functions to get this result.