varSamp

Calculate the sample variance of a data set.

Syntax

varSamp(x)

Alias: VAR_SAMP.

Parameters

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

Returned value

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

Implementation details

The varSamp function calculates the sample variance using the following formula:

\sum\frac{(x - \text{mean}(x))^2}{(n - 1)}

Where:

x is each individual data point in the data set.
mean(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.

Example

Query:

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;

Response:

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

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

Note

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

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​

varSamp

varSamp