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> Computes an approximate quantile of a sample consisting of bfloat16 numbers.

# quantileBFloat16

<h2 id="quantileBFloat16">
  quantileBFloat16
</h2>

Introduced in: v21.7.0

Computes an approximate [quantile](https://en.wikipedia.org/wiki/Quantile) of a sample consisting of [bfloat16](https://en.wikipedia.org/wiki/Bfloat16_floating-point_format) numbers.

`bfloat16` is a floating-point data type with 1 sign bit, 8 exponent bits and 7 fraction bits.
The function converts input values to 32-bit floats and takes the most significant 16 bits. Then it calculates `bfloat16` quantile value and converts the result to a 64-bit float by appending zero bits.
The function is a fast quantile estimator with a maximum relative error of `0.78125%` (and an average relative error of approximately `0.27%`), corresponding to the 7-bit mantissa precision of `bfloat16`.

**Syntax**

```sql theme={null}
quantileBFloat16[(level)](expr)
```

**Aliases**: `medianBFloat16`

**Parameters**

* `level` — Optional. Level of quantile. Possible values are in the range from 0 to 1. Default value: 0.5. [`Float*`](/reference/data-types/float)

**Arguments**

* `expr` — Column with numeric data. [`(U)Int*`](/reference/data-types/int-uint) or [`Float*`](/reference/data-types/float)

**Returned value**

Approximate quantile of the specified level. [`Float64`](/reference/data-types/float)

**Examples**

**Computing quantile with bfloat16**

```sql title=Query theme={null}
CREATE TABLE example_table (a UInt32, b Float32) ENGINE = Memory;
INSERT INTO example_table VALUES (1, 1.001), (2, 1.002), (3, 1.003), (4, 1.004);

SELECT quantileBFloat16(0.75)(a), quantileBFloat16(0.75)(b) FROM example_table;
```

```response title=Response theme={null}
┌─quantileBFloat16(0.75)(a)─┬─quantileBFloat16(0.75)(b)─┐
│                         3 │                         1 │
└───────────────────────────┴───────────────────────────┘
```

**See Also**

* [median](/reference/functions/aggregate-functions/median)
* [quantiles](/reference/functions/aggregate-functions/quantiles)