9.1.2  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,…,x_n] with mean µ = (x₁ + ⋯ + x_n)/n, the variance is

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

  ⎤ ⎥ ⎥ ⎦