varPop

Calculates the population variance:

\frac{\Sigma{(x - \bar{x})^2}}{n}

Syntax

varPop(x)

Alias: VAR_POP.

Parameters

x: Population of values to find the population variance of. (U)Int*, Float*, Decimal*.

Returned value

Returns the population variance of x. Float64.

Example

Query:

DROP TABLE IF EXISTS test_data;
CREATE TABLE test_data
(
    x UInt8,
)
ENGINE = Memory;

INSERT INTO test_data VALUES (3), (3), (3), (4), (4), (5), (5), (7), (11), (15);

SELECT
    varPop(x) AS var_pop
FROM test_data;

Result:

┌─var_pop─┐
│    14.4 │
└─────────┘

varPop

Introduced in: v1.1

Calculates the population variance.

The population variance is calculated using the formula:

\frac{\Sigma{(x - \bar{x})^2}}{n}

Where:

$x$ is each value in the population
$\bar{x}$ is the population mean
$n$ is the population size

Note

This function uses a numerically unstable algorithm. If you need numerical stability in calculations, use the varPopStable function. It works slower but provides a lower computational error.

Syntax

varPop(x)

Aliases: VAR_POP

Arguments

x — Population of values to find the population variance of. (U)Int* or Float* or Decimal*

Returned value

Returns the population variance of x. Float64

Examples

Computing population variance

DROP TABLE IF EXISTS test_data;
CREATE TABLE test_data
(
    x UInt8,
)
ENGINE = Memory;

INSERT INTO test_data VALUES (3), (3), (3), (4), (4), (5), (5), (7), (11), (15);

SELECT
    varPop(x) AS var_pop
FROM test_data;

┌─var_pop─┐
│    14.4 │
└─────────┘

varPop​

varPop​

varPop

varPop