# Variance: variance

### 8.1.2 Variance: 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

(x1 − µ)2 + … + (xn − µ)2
n

.

The squares help ensure that the numbers above the mean and those below the mean don’t 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.

- Input:
  variance([1,2,3,4])
  Output:

  5
  4

- Input:
  variance([[1,2,3],[5,6,7]])
  Output:

  ⎡ ⎣ | 4,4,4 | ⎤ ⎦

- Input:
  variance([2,4,6,8],[2,2,3,3])
  Output:

  121
  25

- Input:
  variance([[1,2],[3,4]],[[1,2],[2,1]])
  Output:

  ⎡
  ⎢
  ⎢
  ⎣

  8
  9

  ,

  8
  9

  ⎤
  ⎥
  ⎥
  ⎦