quantileExact

Exactly computes the quantile of a numeric data sequence.

To get exact value, all the passed values ​​are combined into an array, which is then partially sorted. Therefore, the function consumes O(n) memory, where n is a number of values that were passed. However, for a small number of values, the function is very effective.

When using multiple quantile* functions with different levels in a query, the internal states are not combined (that is, the query works less efficiently than it could). In this case, use the quantiles function.

Syntax

quantileExact(level)(expr)

Alias: medianExact.

Parameters

• level — Level of quantile. Optional parameter. Constant floating-point number from 0 to 1. We recommend using a level value in the range of [0.01, 0.99]. Default value: 0.5. At level=0.5 the function calculates median.
• expr — Expression over the column values resulting in numeric data types, Date or DateTime.

Returned value

• Quantile of the specified level.

Type:

• Float64 for numeric data type input.
• Date if input values have the Date type.
• DateTime if input values have the DateTime type.

Example

Query:

SELECT quantileExact(number) FROM numbers(10)

Result:

┌─quantileExact(number)─┐
│                     5 │
└───────────────────────┘

quantileExactLow

Similar to quantileExact, this computes the exact quantile of a numeric data sequence.

To get exact value, all the passed values are combined into an array, which is then fully sorted. The sorting algorithm’s complexity is O(N·log(N)), where N = std::distance(first, last) comparisons.

Depending on the level, i.e if the level is 0.5 then the exact lower median value is returned if there are even number of elements and the middle value is returned if there are odd number of elements. Median is calculated similar to the median_low implementation which is used in python.

For all other levels, the element at the the index corresponding to the value of level * size_of_array is returned. For example:

```$sql
SELECT quantileExactLow(0.1)(number) FROM numbers(10)

┌─quantileExactLow(0.1)(number)─┐
│ 1 │
└───────────────────────────────┘

When using multiple `quantile*` functions with different levels in a query, the internal states are not combined (that is, the query works less efficiently than it could). In this case, use the [quantiles](../../../sql-reference/aggregate-functions/reference/quantiles.md#quantiles) function.
**Syntax**
``` sql
quantileExact(level)(expr)

Alias: medianExactLow.

Parameters

• level — Level of quantile. Optional parameter. Constant floating-point number from 0 to 1. We recommend using a level value in the range of [0.01, 0.99]. Default value: 0.5. At level=0.5 the function calculates median.
• expr — Expression over the column values resulting in numeric data types, Date or DateTime.

Returned value

• Quantile of the specified level.

Type:

• Float64 for numeric data type input.
• Date if input values have the Date type.
• DateTime if input values have the DateTime type.

Example

Query:

SELECT quantileExactLow(number) FROM numbers(10)

Result:

┌─quantileExactLow(number)─┐
│                        4 │
└──────────────────────────┘

quantileExactHigh

Similar to quantileExact, this computes the exact quantile of a numeric data sequence.

To get exact value, all the passed values are combined into an array, which is then fully sorted. The sorting algorithm’s complexity is O(N·log(N)), where N = std::distance(first, last) comparisons.

Depending on the level, i.e if the level is 0.5 then the exact higher median value is returned if there are even number of elements and the middle value is returned if there are odd number of elements. Median is calculated similar to the median_high implementation which is used in python. For all other levels, the element at the the index corresponding to the value of level * size_of_array is returned.

This implementation behaves exactly similar to the current quantileExact implementation.

When using multiple quantile* functions with different levels in a query, the internal states are not combined (that is, the query works less efficiently than it could). In this case, use the quantiles function.

Syntax

quantileExactHigh(level)(expr)

Alias: medianExactHigh.

Parameters

• level — Level of quantile. Optional parameter. Constant floating-point number from 0 to 1. We recommend using a level value in the range of [0.01, 0.99]. Default value: 0.5. At level=0.5 the function calculates median.
• expr — Expression over the column values resulting in numeric data types, Date or DateTime.

Returned value

• Quantile of the specified level.

Type:

• Float64 for numeric data type input.
• Date if input values have the Date type.
• DateTime if input values have the DateTime type.

Example

Query:

SELECT quantileExactHigh(number) FROM numbers(10)

Result:

┌─quantileExactHigh(number)─┐
│                         5 │
└───────────────────────────┘

See Also

• median
• quantiles