varSampStable

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 │
└─────────────────┘