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> Calculates the value of the population covariance

# covarPopStable

<h2 id="covarPopStable">
  covarPopStable
</h2>

Introduced in: v1.1.0

Calculates the population covariance:

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

<br />

It is similar to the [`covarPop`](/reference/functions/aggregate-functions/covarPop) function, but uses a numerically stable algorithm. As a result, `covarPopStable` is slower than `covarPop` but produces a more accurate result.

**Syntax**

```sql theme={null}
covarPopStable(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 population covariance between `x` and `y`. [`Float64`](/reference/data-types/float)

**Examples**

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

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