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> Use this file to discover all available pages before exploring further.

> Calculates the value of `Σ((x - x̅)(y - y̅)) / (n - 1)`

# covarSamp

<h2 id="covarSamp">
  covarSamp
</h2>

Introduced in: v1.1.0

Calculates the sample covariance:

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

<Note>
  This function uses a numerically unstable algorithm. If you need [numerical stability](https://en.wikipedia.org/wiki/Numerical_stability) in calculations, use the [`covarSampStable`](/reference/functions/aggregate-functions/covarSampStable) function.
  It works slower but provides a lower computational error.
</Note>

**Syntax**

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

**Aliases**: `COVAR_SAMP`

**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`, `nan` is returned. [`Float64`](/reference/data-types/float)

**Examples**

**Basic sample covariance calculation**

```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 covarSamp(x_value, y_value)
FROM series
```

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

**Single value returns NaN**

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

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