20.1.2 Variance
The variance of a list of numbers measures how close the numbers are
to their mean by finding the average of the squares of the differences
between the numbers and the mean; specifically, given a list of
numbers [x1,…,xn] with mean µ=(x1+⋯+xn)/n,
the variance is
The squares help ensure that the numbers above the mean and those
below the mean do not cancel out.
The variance command
computes the variance.
-
variance takes one mandatory argument and one optional
argument:
-
L, a list or matrix of numbers.
- W, a list or matrix of weights, the same size as L.
- variance(L ⟨,W⟩) returns the variance
of the list or a list with the variances of the columns of the matrix.
Examples
| variance([[1,2,3],[5,6,7]]) |
| variance([2,4,6,8],[2,2,3,3]) |
| variance([[1,2],[3,4]],[[1,2],[2,1]]) |