ClickHouse/docs/en/sql-reference/aggregate-functions/reference/varsamp.md

title	slug	sidebar_position
varSamp	/en/sql-reference/aggregate-functions/reference/varsamp	33

varSamp

Calculate the sample variance of a 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)

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 │
└──────────┘