> ## Documentation Index
> Fetch the complete documentation index at: https://private-7c7dfe99-mintlify-3a82795f.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

> Similar to covarSamp but works slower while providing a lower computational error.

# covarSampStable

<h2 id="covarSampStable">
  covarSampStable
</h2>

Introduced in: v1.1.0

Calculates the sample covariance:

$$
\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{n - 1}
$$

<br />

It is similar to [`covarSamp`](/reference/functions/aggregate-functions/covarSamp) but uses a numerically stable algorithm.
As a result, `covarSampStable` is slower than `covarSamp` but provides a lower computational error.

**Syntax**

```sql theme={null}
covarSampStable(x, y)
```

**Arguments**

* `x` — First variable. [`(U)Int*`](/reference/data-types/int-uint) or [`Float*`](/reference/data-types/float) or [`Decimal`](/reference/data-types/decimal)
* `y` — Second variable. [`(U)Int*`](/reference/data-types/int-uint) or [`Float*`](/reference/data-types/float) or [`Decimal`](/reference/data-types/decimal)

**Returned value**

Returns the sample covariance between `x` and `y`. For `n <= 1`, `inf` is returned. [`Float64`](/reference/data-types/float)

**Examples**

**Basic sample covariance calculation with stable algorithm**

```sql title=Query theme={null}
DROP TABLE IF EXISTS series;
CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);

SELECT covarSampStable(x_value, y_value)
FROM
(
    SELECT
        x_value,
        y_value
    FROM series
);
```

```response title=Response theme={null}
┌─covarSampStable(x_value, y_value)─┐
│                 7.206275555555556 │
└───────────────────────────────────┘
```

**Single value returns inf**

```sql title=Query theme={null}
SELECT covarSampStable(x_value, y_value)
FROM
(
    SELECT
        x_value,
        y_value
    FROM series LIMIT 1
);
```

```response title=Response theme={null}
┌─covarSampStable(x_value, y_value)─┐
│                               inf │
└───────────────────────────────────┘
```