varSamp

Introduced in: v1.1

Calculate the sample variance of a data set.

The sample variance is calculated using the formula:

\frac{\Sigma{(x - \bar{x})^2}}{n-1}

Where:

$x$ is each individual data point in the data set
$\bar{x}$ is the arithmetic mean of the data set
$n$ is the number of data points in the data set

The function assumes that the input data set represents a sample from a larger population. If you want to calculate the variance of the entire population (when you have the complete data set), you should use varPop instead.

Примечание

Функция использует численно неустойчивый алгоритм. Если требуется численная устойчивость вычислений, используйте функцию varSampStable. Она работает медленнее, но обеспечивает меньшую вычислительную погрешность.

Syntax

varSamp(x)

Aliases: VAR_SAMP

Arguments

x — The population for which you want to calculate the sample variance. (U)Int* or Float* or Decimal*

Returned value

Returns the sample variance of the input data set x. Float64

Examples

Computing sample variance

DROP TABLE IF EXISTS test_data;
CREATE TABLE test_data
(
    x Float64
)
ENGINE = Memory;

INSERT INTO test_data VALUES (10.5), (12.3), (9.8), (11.2), (10.7);

SELECT round(varSamp(x),3) AS var_samp FROM test_data;

┌─var_samp─┐
│    0.865 │
└──────────┘

varSamp​

varSamp