var

Aggregation functions > var

syntax

• var(values_attribute)
• var(values_attribute, relation)

description

The var function calculates the variance of the values in values_attribute.

When called with a single argument, it calculates the total variance across all elements.

When called with a relation argument, it calculates the variance per group defined by the relation, producing a partitioned result.

The variance is calculated using the formula:

var = Σ(x - μ)² / n

where μ is the mean and n is the count of defined values.

Note: This calculates the population variance. For sample variance (dividing by n-1), use: var(x) * count(x) / (count(x) - 1).

applies to

• attribute values_attribute with a numeric value type (Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Float32, Float64)
• attribute relation (optional) with a relation to the grouping domain

conditions

1. The values_attribute must have a numeric value type.
2. If specified, relation must define a valid grouping.
3. Null values in values_attribute are excluded from the calculation.

result

• Without relation: a parameter with Float64 value type
• With relation: an attribute with Float64 value type and the domain of the relation's values unit

performance

aspect	indication
time complexity	O(n) where n = number of elements
memory	O(1) for total, O(k) for partitioned where k = number of groups
parallelization	tiled parallel processing supported

The calculation uses a numerically stable two-pass algorithm (first for mean, second for variance).

since version

1.0

example

total variance

unit<uint32> Person: nrofrows = 5
{
   attribute<float32> age: [25, 30, 35, 40, 45];
}

parameter<float64> age_variance := var(Person/age);
// Result: 50.0 (population variance)

partitioned variance

unit<uint32> Person: nrofrows = 6
{
   attribute<float32> salary: [50000, 55000, 60000, 45000, 48000, 52000];
   attribute<Region>  region_rel: [0, 0, 0, 1, 1, 1];
}

unit<uint32> Region: nrofrows = 2;

attribute<float64> salary_var_per_region (Region) := var(Person/salary, Person/region_rel);
// Result: [16666666.67, 8222222.22] (variance per region)

see also

• sd - standard deviation (square root of variance)
• mean - arithmetic mean
• covariance - covariance between two attributes
• correlation - correlation coefficient

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