# MEDIAN

Syntax Description of the illustration median.gif

See Also:

"Analytic Functions" for information on syntax, semantics, and restrictions

Purpose

`MEDIAN` is an inverse distribution function that assumes a continuous distribution model. It takes a numeric or datetime value and returns the middle value or an interpolated value that would be the middle value once the values are sorted. Nulls are ignored in the calculation.

This function takes as arguments any numeric datatype or any nonnumeric datatype that can be implicitly converted to a numeric datatype. If you specify only `expr`, then the function returns the same datatype as the numeric datatype of the argument. if you specify the `OVER` clause, then Oracle Database determines the argument with the highest numeric precedence, implicitly converts the remaining arguments to that datatype, and returns that datatype.

See Also:

Table 2-10, "Implicit Type Conversion Matrix" for more information on implicit conversion and "Numeric Precedence" for information on numeric precedence

The result of `MEDIAN` is computed by first ordering the rows. Using `N` as the number of rows in the group, Oracle calculates the row number (`RN`) of interest with the formula `RN` = (`1` + (0.`5`*(`N`-`1`)). The final result of the aggregate function is computed by linear interpolation between the values from rows at row numbers `CRN` = `CEILING`(`RN`) and `FRN` = `FLOOR`(`RN`).

The final result will be:

```   if (CRN = FRN = RN) then
(value of expression from row at RN)
else
(CRN - RN) * (value of expression for row at FRN) +
(RN - FRN) * (value of expression for row at CRN)

```

You can use `MEDIAN` as an analytic function. You can specify only the `query_partition_clause` in its `OVER` clause. It returns, for each row, the value that would fall in the middle among a set of values within each partition.

Compare this function with these functions:

• PERCENTILE_CONT, which returns, for a given percentile, the value that corresponds to that percentile by way of interpolation. `MEDIAN` is the specific case of `PERCENTILE_CONT` where the percentile value defaults to 0.5.

• PERCENTILE_DISC, which is useful for finding values for a given percentile without interpolation.

Aggregate Example

The following query returns the median salary for each department in the `hr.employees` table:

```SELECT department_id, MEDIAN(salary)
FROM employees
GROUP BY department_id;

DEPARTMENT_ID MEDIAN(SALARY)
------------- --------------
10           4400
20           9500
30           2850
40           6500
50           3100
60           4800
70          10000
80           8900
90          17000
100           8000
110          10150
7000
```

Analytic Example

The following query returns the median salary for each manager in a subset of departments in the `hr.employees` table:

```SELECT manager_id, employee_id, salary,
MEDIAN(salary) OVER (PARTITION BY manager_id) "Median by Mgr"
FROM employees
WHERE department_id > 60;

MANAGER_ID EMPLOYEE_ID     SALARY Median by Mgr
---------- ----------- ---------- -------------
100         149      10500         13500
100         148      11000         13500
100         147      12000         13500
100         146      13500         13500
100         145      14000         13500
100         101      17000         13500
100         102      17000         13500
101         204      10000         12000
101         108      12000         12000
101         205      12000         12000
108         113       6900          7800
108         111       7700          7800
108         112       7800          7800
108         110       8200          7800
108         109       9000          7800
145         155       7000          8500
145         154       7500          8500
. . .
```