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

> Calculates the population covariance

# covarPop

<h2 id="covarPop">
  covarPop
</h2>

Introduced in: v1.1.0

Calculates the population covariance:

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

<br />

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

**Syntax**

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

**Aliases**: `COVAR_POP`

**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 population covariance between `x` and `y`. [`Float64`](/reference/data-types/float)

**Examples**

**Basic population 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 covarPop(x_value, y_value)
FROM series
```

```response title=Response theme={null}
┌─covarPop(x_value, y_value)─┐
│                   6.485648 │
└────────────────────────────┘
```