# Standard deviation: stdev

### 8.1.3 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

√

(1−5/2)2 + (2−5/2)2 + (3−5/2)2 + (4−5/2)2
4

=

2

√

5

4

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 | ⎤ ⎦