Population and sample variance of a data vector

s-tilde^2 with the 1/n divisor, the unbiased s^2 with 1/(n-1), and the computational identity. Mirrors morie.fn ...3e37/3e60/3e66/3e73.

Usage

morie_data_variance(x)

Arguments

x

numeric data, length >= 2.

Value

list(mean, population_variance, sample_variance).

References

Morin (2016), eqs. (3.37), (3.60), (3.66), (3.73).

Examples

morie_data_variance(c(2, 4, 4, 4, 5, 5, 7, 9))$population_variance
#> [1] 4