# The mean: mean

### 8.1.1 The mean: mean

Recall that the mean of a list x1,…,xn is simply their numeric average (x1 + ⋯ + xn)/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.