## 9.2 Statistical Aggregate Functions

### 9.2.1 `CORR`

Available inDSQL, PSQL

Result type`DOUBLE PRECISION`

Syntax

````CORR ( <expr1>, <expr2> )`
```

The `CORR` function return the correlation coefficient for a pair of numerical expressions.

The function `CORR(<expr1>, <expr2>)` is equivalent to

````COVAR_POP(<expr1>, <expr2>) / (STDDEV_POP(<expr2>) * STDDEV_POP(<expr1>))`
```

This is also known as the Pearson correlation coefficient.

In a statistical sense, correlation is the degree of to which a pair of variables are linearly related. A linear relation between variables means that the value of one variable can to a certain extent predict the value of the other. The correlation coefficient represents the degree of correlation as a number ranging from -1 (high inverse correlation) to 1 (high correlation). A value of 0 corresponds to no correlation.

If the group or window is empty, or contains only `NULL` values, the result will be `NULL`.

#### 9.2.1.1 `CORR` Examples

````select`
`  corr(alength, aheight) AS c_corr`
`from measure`
```

### 9.2.2 `COVAR_POP`

Available inDSQL, PSQL

Result type`DOUBLE PRECISION`

Syntax

````COVAR_POP ( <expr1>, <expr2> )`
```

The function `COVAR_POP` returns the population covariance for a pair of numerical expressions.

The function `COVAR_POP(<expr1>, <expr2>)` is equivalent to

````(SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / COUNT(*)`
```

If the group or window is empty, or contains only `NULL` values, the result will be `NULL`.

#### 9.2.2.1 `COVAR_POP` Examples

````select`
`  covar_pop(alength, aheight) AS c_covar_pop`
`from measure`
```

### 9.2.3 `COVAR_SAMP`

Available inDSQL, PSQL

Result type`DOUBLE PRECISION`

Syntax

````COVAR_SAMP ( <expr1>, <expr2> )`
```

The function `COVAR_SAMP` returns the sample covariance for a pair of numerical expressions.

The function `COVAR_SAMP(<expr1>, <expr2>)` is equivalent to

````(SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / (COUNT(*) - 1)`
```

If the group or window is empty, contains only 1 row, or contains only `NULL` values, the result will be `NULL`.

#### 9.2.3.1 `COVAR_SAMP` Examples

````select`
`  covar_samp(alength, aheight) AS c_covar_samp`
`from measure`
```

### 9.2.4 `STDDEV_POP`

Available inDSQL, PSQL

Result type`DOUBLE PRECISION` or `NUMERIC` depending on the type of expr

Syntax

````STDDEV_POP ( <expr> )`
```

The function `STDDEV_POP` returns the population standard deviation for a group or window. `NULL` values are skipped.

The function `STDDEV_POP(<expr>)` is equivalent to

````SQRT(VAR_POP(<expr>))`
```

If the group or window is empty, or contains only `NULL` values, the result will be `NULL`.

#### 9.2.4.1 `STDDEV_POP` Examples

````select`
`  dept_no`
`  stddev_pop(salary)`
`from employee`
`group by dept_no`
```

### 9.2.5 `STDDEV_SAMP`

Available inDSQL, PSQL

Result type`DOUBLE PRECISION` or `NUMERIC` depending on the type of expr

Syntax

````STDDEV_POP ( <expr> )`
```

The function `STDDEV_SAMP` returns the sample standard deviation for a group or window. `NULL` values are skipped.

The function `STDDEV_SAMP(<expr>)` is equivalent to

````SQRT(VAR_SAMP(<expr>))`
```

If the group or window is empty, contains only 1 row, or contains only `NULL` values, the result will be `NULL`.

#### 9.2.5.1 `STDDEV_SAMP` Examples

````select`
`  dept_no`
`  stddev_samp(salary)`
`from employee`
`group by dept_no`
```

### 9.2.6 `VAR_POP`

Available inDSQL, PSQL

Result type`DOUBLE PRECISION` or `NUMERIC` depending on the type of expr

Syntax

````VAR_POP ( <expr> )`
```

The function `VAR_POP` returns the population variance for a group or window. `NULL` values are skipped.

The function `VAR_POP(<expr>)` is equivalent to

````(SUM(<expr> * <expr>) - SUM (<expr>) * SUM (<expr>) / COUNT(<expr>))`
`  / COUNT (<expr>)`
```

If the group or window is empty, or contains only `NULL` values, the result will be `NULL`.

#### 9.2.6.1 `VAR_POP` Examples

````select`
`  dept_no`
`  var_pop(salary)`
`from employee`
`group by dept_no`
```

### 9.2.7 `VAR_SAMP`

Available inDSQL, PSQL

Result type`DOUBLE PRECISION` or `NUMERIC` depending on the type of expr

Syntax

````VAR_SAMP ( <expr> )`
```

The function `VAR_POP` returns the sample variance for a group or window. `NULL` values are skipped.

The function `VAR_SAMP(<expr>)` is equivalent to

````(SUM(<expr> * <expr>) - SUM(<expr>) * SUM (<expr>) / COUNT (<expr>))`
`  / (COUNT(<expr>) - 1)`
```

If the group or window is empty, contains only 1 row, or contains only `NULL` values, the result will be `NULL`.

#### 9.2.7.1 `VAR_SAMP` Examples

````select`
`  dept_no`
`  var_samp(salary)`
`from employee`
`group by dept_no`
```