9.1.3  Standard deviation: stdev

Standard deviation is potentially better than variance to measure how close numbers are to their mean. The standard deviation is the square root of the variance; for example, the list [1,2,3,4] has mean 5/2, and so the standard deviation will be 2√5/4, since

Note that if the list of numbers have units, then the standard deviation will have the same unit.

The stddev command finds the standard deviation.

• stddev 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.
• stddev(L ⟩ W⟨) returns the standard deviation of the list or a list with the standard deviations of the columns of the matrix.

Examples.

• Input:
  stddev([1,2,3,4])
  Output:

  √ 5 2

• Input:
  stddev([1,2,3],[2,1,1])
  Output:

  4 16

  √

  11

• Input:
  stddev([[1,2],[3,6]])
  Output:

  ⎡ ⎣

  1,2

  ⎤ ⎦