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> Computes an approximate quantile of a numeric data sequence using the t-digest algorithm.

# quantileTDigest

<h2 id="quantileTDigest">
  quantileTDigest
</h2>

Introduced in: v1.1.0

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`](/reference/functions/aggregate-functions/quantile) or [`quantileTiming`](/reference/functions/aggregate-functions/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`](/reference/functions/aggregate-functions/quantiles#quantiles) function.

**Syntax**

```sql theme={null}
quantileTDigest(level)(expr)
```

**Aliases**: `medianTDigest`

**Parameters**

* `level` — Optional. Level of quantile. 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. [`Float*`](/reference/data-types/float)

**Arguments**

* `expr` — Expression over the column values resulting in numeric data types, Date or DateTime. [`(U)Int*`](/reference/data-types/int-uint) or [`Float*`](/reference/data-types/float) or [`Decimal*`](/reference/data-types/decimal) or [`Date`](/reference/data-types/date) or [`DateTime`](/reference/data-types/datetime)

**Returned value**

Approximate quantile of the specified level. [`Float64`](/reference/data-types/float) or [`Date`](/reference/data-types/date) or [`DateTime`](/reference/data-types/datetime)

**Examples**

**Computing quantile with t-digest**

```sql title=Query theme={null}
SELECT quantileTDigest(number) FROM numbers(10);
```

```response title=Response theme={null}
┌─quantileTDigest(number)─┐
│                     4.5 │
└─────────────────────────┘
```

**See Also**

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