---
description: 'Computes an approximate quantile of a numeric data sequence using the
  t-digest algorithm.'
sidebar_position: 178
slug: /sql-reference/aggregate-functions/reference/quantiletdigest
title: 'quantileTDigest'
---

# quantileTDigest

Computes an approximate [quantile](https://en.wikipedia.org/wiki/Quantile) of a numeric data sequence using the [t-digest](https://github.com/tdunning/t-digest/blob/master/docs/t-digest-paper/histo.pdf) algorithm.

Memory consumption is `log(n)`, where `n` is a number of values. The result depends on the order of running the query, and is nondeterministic.

The performance of the function is lower than performance of [quantile](/sql-reference/aggregate-functions/reference/quantile) or [quantileTiming](/sql-reference/aggregate-functions/reference/quantiletiming). In terms of the ratio of State size to precision, this function is much better than `quantile`.

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
quantileTDigest(level)(expr)
```

Alias: `medianTDigest`.

**Arguments**

- `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), [Date](../../../sql-reference/data-types/date.md) or [DateTime](../../../sql-reference/data-types/datetime.md).

**Returned value**

- Approximate 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 quantileTDigest(number) FROM numbers(10)
```

Result:

```text
┌─quantileTDigest(number)─┐
│                     4.5 │
└─────────────────────────┘
```

**See Also**

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