varSampStable

Calculate the sample variance of a data set. Unlike varSamp, this function uses a numerically stable algorithm. It works slower but provides a lower computational error.

Syntax

varSampStable(x)

Alias: VAR_SAMP_STABLE

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. Float64.

Implementation details

The varSampStable function calculates the sample variance using the same formula as the varSamp:

\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.

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(varSampStable(x),3) AS var_samp_stable FROM test_data;

Response:

┌─var_samp_stable─┐
│           0.865 │
└─────────────────┘

varSampStable

Introduced in: v1.1

Calculate the sample variance of a data set. Unlike varSamp, this function uses a numerically stable algorithm. It works slower but provides a lower computational error.

The sample variance is calculated using the same formula as varSamp:

\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

Syntax

varSampStable(x)

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. Float64

Examples

Computing stable 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(varSampStable(x),3) AS var_samp_stable FROM test_data;

┌─var_samp_stable─┐
│           0.865 │
└─────────────────┘

varSampStable​

varSampStable​

varSampStable

varSampStable