Reference · Statistics

stats.variance

stats.variance(list, num | null=) -> float

What it does

The sample variance of a list of numbers: the sum of the squared distances from the mean, divided by one less than the count (Bessel's correction). It is Python's statistics.variance, for data that is a sample of a larger population; for the whole population use stats.pvariance. The answer is a float, computed with compensated sums so it is Python's exact result.

Examples

print(stats.variance([1, 2, 3, 4]))print(stats.variance([2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]))

1.66666666666666671.3720238095238095

Edge cases

• At least two numbers are needed: one number is an error, not 0.0.
• A constant list gives 0.0.
• A second argument, a mean already known, is accepted, but the answer is the spread about the data's own mean whatever is given, as in Python before 3.11: a correction in the sum cancels the difference. Leave it out, or pass null.
• The sample variance of two lists that are the same is their covariance.

print(stats.variance([7, 7, 7]), stats.variance([1.0, 2.0]))print(stats.variance([1, 2, 3, 4], 0), stats.variance([1, 2, 3, 4], 2.5), stats.variance([1, 2, 3, 4], null))print(stats.variance([1, 2, 3]) == stats.covariance([1, 2, 3], [1, 2, 3]))

0.0 0.51.6666666666666667 1.6666666666666667 1.6666666666666667true

Errors

Fewer than two numbers is a runtime error, not an error value: an empty list, null or a list of one stops the request. So does an item that is not a number.

print(stats.variance([5]))

line 1: `stats.variance` requires at least 2 data points

print(stats.variance([]))

line 1: `stats.variance` requires at least 2 data points

Chaining

let xs = [2, 4, 4, 4, 5, 5, 7, 9]print(xs | stats.variance | round(3))print(len(xs) > 1 && (xs | stats.variance) > 0)

4.571true

See also

stats.pvariance, stats.stdev, stats.pstdev, stats.covariance, stats.mean

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