9.1.1  The mean: mean

Recall that the mean of a list x₁,…,x_n is simply their numeric average (x₁ + ⋯ + x_n)/n. The mean command finds the mean of a list.

• mean 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.
• mean(L ⟩ W⟨) returns the mean of the list or a list with the means of the columns of the matrix.

Examples.

• Input:
  mean([1,2,3,4])
  Output:

  5 2

  since (1+2+3+4)/4 = 5/2.
• Input:
  mean([[1,2,3],[5,6,7]])
  Output:

  ⎡ ⎣

  3,4,5

  ⎤ ⎦

  since (1+5)/2 = 3, (2+6)/2 = 4 and (3 + 7)/2 = 5.
• Input:
  mean([2,4,6,8],[2,2,3,3])
  Output:

  27 5

  since (2· 2 + 4· 2 + 6· 3 + 8· 3)/(2 + 2 + 3 + 3) = 27/5.
• Input:
  mean([[1,2],[3,4]],[[1,2],[2,1]])
  Output:

  ⎡ ⎢ ⎢ ⎣

  7 3

  ,

  8 3

  ⎤ ⎥ ⎥ ⎦

  since (1· 1 + 3· 2)/(1+2) = 7/3 and (2· 2 + 4· 1)/(2 + 1) = 8/3.