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> Computes multiple approximate quantiles using the t-digest algorithm at different levels simultaneously.

# quantilesTDigest

<h2 id="quantilesTDigest">
  quantilesTDigest
</h2>

Introduced in: v1.1.0

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

This function is equivalent to [`quantileTDigest`](/reference/functions/aggregate-functions/quantileTDigest) but allows computing multiple quantile levels in a single pass, which is more efficient than calling individual quantile functions.

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 [`quantiles`](/reference/functions/aggregate-functions/quantiles) or [`quantilesTiming`](/reference/functions/aggregate-functions/quantilesTiming). In terms of the ratio of State size to precision, this function is much better than `quantiles`.

**Syntax**

```sql theme={null}
quantilesTDigest(level1, level2, ...)(expr)
```

**Parameters**

* `level` — Levels of quantiles. One or more constant floating-point numbers from 0 to 1. We recommend using `level` values in the range of `[0.01, 0.99]`. [`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 [`Date`](/reference/data-types/date) or [`DateTime`](/reference/data-types/datetime)

**Returned value**

Array of approximate quantiles of the specified levels in the same order as the levels were specified. For `Date` and `DateTime` inputs the output format matches the input format. [`Array(Float32)`](/reference/data-types/array) or [`Array(Date)`](/reference/data-types/array) or [`Array(DateTime)`](/reference/data-types/array)

**Examples**

**Computing multiple quantiles with t-digest**

```sql title=Query theme={null}
SELECT quantilesTDigest(0.25, 0.5, 0.75)(number) FROM numbers(100);
```

```response title=Response theme={null}
┌─quantilesTDigest(0.25, 0.5, 0.75)(number)─┐
│ [24.75,49.5,74.25]                        │
└───────────────────────────────────────────┘
```