Statistic functions : mean,variance,stddev, stddevp,median,quantile,quartiles,boxwhisker

The functions described here may be used if the statistic serie is contained in a list. See also section 1.42.31 for matrices and chapter for weighted lists.

• mean computes the arithmetic mean of a list
  Input :
  mean([3,4,2])
  Output :
  3
  Input :
  mean([1,0,1])
  Output
  2/3
• stddev computes the standard deviation of a population, if the argument is the population
  Input :
  stddev([3,4,2])
  Output :
  sqrt(2/3)
• stddevp computes an unbiaised estimate of the standard deviation of the population, if the argument is a sample. The following relation holds:
  stddevp(l)^2=size(l)*stddev(l)^2/(size(l)-1).
  Input :
  stddevp([3,4,2])
  Output :
  1
• variance computes the variance of a list, that is the square of stddevp
  Input :
  variance([3,4,2])
  Output :
  2/3
• median computes the median of a list.
  Input :
  median([0,1,3,4,2,5,6])
  Output :
  3.0
• quantile computes the deciles of a list given as first argument, where the decile is the second argument.
  Input :
  quantile([0,1,3,4,2,5,6],0.25)
  Output the first quartile :
  [1.0]
  Input :
  quantile([0,1,3,4,2,5,6],0.5)
  Output the median :
  [3.0]
  Input :
  quantile([0,1,3,4,2,5,6],0.75)
  Output the third quartile :
  [4.0]
• quartiles computes the minimum, the first quartile, the median, the third quartile and the maximum of a list.
  Input :
  quartiles([0,1,3,4,2,5,6])
  Output :
  [[0.0],[1.0],[3.0],[4.0],[6.0]]
• boxwhisker draws the whisker box of a statistic serie stored in a list.
  Input :
  boxwhisker([0,1,3,4,2,5,6])
  Output
  the graph of the whisker box of this statistic list

Example
Define the list A by:

A:=[0,1,2,3,4,5,6,7,8,9,10,11]

Outputs :

1. 11/2 for mean(A)
2. sqrt(143/12) for stddev(A)
3. 0 for min(A)
4. [1.0] for quantile(A,0.1)
5. [2.0] for quantile(A,0.25)
6. [5.0] for median(A) or for quantile(A,0.5)
7. [8.0] for quantile(A,0.75)
8. [9.0] for quantile(A,0.9)
9. 11 for max(A)
10. [[0.0],[2.0],[5.0],[8.0],[11.0]] for quartiles(A)