ClickHouse/docs/en/sql-reference/aggregate-functions/reference/quantileexact.md

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toc_priority: 202
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# quantileExact {#quantileexact}

Exactly computes the [quantile](https://en.wikipedia.org/wiki/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](../../../sql-reference/aggregate-functions/reference/quantiles.md#quantiles) function.

**Syntax**

``` sql
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](https://en.wikipedia.org/wiki/Median).
-   `expr` — Expression over the column values resulting in numeric [data types](../../../sql-reference/data-types/index.md#data_types), [Date](../../../sql-reference/data-types/date.md) or [DateTime](../../../sql-reference/data-types/datetime.md).

**Returned value**

-   Quantile of the specified level.

Type:

-   [Float64](../../../sql-reference/data-types/float.md) for numeric data type input.
-   [Date](../../../sql-reference/data-types/date.md) if input values have the `Date` type.
-   [DateTime](../../../sql-reference/data-types/datetime.md) if input values have the `DateTime` type.

**Example**

Query:

``` sql
SELECT quantileExact(number) FROM numbers(10)
```

Result:

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

# quantileExactLow {#quantileexactlow}

Similar to `quantileExact`, this computes the exact [quantile](https://en.wikipedia.org/wiki/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](https://en.cppreference.com/w/cpp/algorithm/sort) 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](https://docs.python.org/3/library/statistics.html#statistics.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](https://en.wikipedia.org/wiki/Median).
-   `expr` — Expression over the column values resulting in numeric [data types](../../../sql-reference/data-types/index.md#data_types), [Date](../../../sql-reference/data-types/date.md) or [DateTime](../../../sql-reference/data-types/datetime.md).

**Returned value**

-   Quantile of the specified level.

Type:

-   [Float64](../../../sql-reference/data-types/float.md) for numeric data type input.
-   [Date](../../../sql-reference/data-types/date.md) if input values have the `Date` type.
-   [DateTime](../../../sql-reference/data-types/datetime.md) if input values have the `DateTime` type.

**Example**

Query:

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

Result:

``` text
┌─quantileExactLow(number)─┐
│                        4 │
└──────────────────────────┘
```
# quantileExactHigh {#quantileexacthigh}

Similar to `quantileExact`, this computes the exact [quantile](https://en.wikipedia.org/wiki/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](https://en.cppreference.com/w/cpp/algorithm/sort) 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](https://docs.python.org/3/library/statistics.html#statistics.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](../../../sql-reference/aggregate-functions/reference/quantiles.md#quantiles) function.

**Syntax**

``` sql
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](https://en.wikipedia.org/wiki/Median).
-   `expr` — Expression over the column values resulting in numeric [data types](../../../sql-reference/data-types/index.md#data_types), [Date](../../../sql-reference/data-types/date.md) or [DateTime](../../../sql-reference/data-types/datetime.md).

**Returned value**

-   Quantile of the specified level.

Type:

-   [Float64](../../../sql-reference/data-types/float.md) for numeric data type input.
-   [Date](../../../sql-reference/data-types/date.md) if input values have the `Date` type.
-   [DateTime](../../../sql-reference/data-types/datetime.md) if input values have the `DateTime` type.

**Example**

Query:

``` sql
SELECT quantileExactHigh(number) FROM numbers(10)
```

Result:

``` text
┌─quantileExactHigh(number)─┐
│                         5 │
└───────────────────────────┘
```
**See Also**

-   [median](../../../sql-reference/aggregate-functions/reference/median.md#median)
-   [quantiles](../../../sql-reference/aggregate-functions/reference/quantiles.md#quantiles)