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14. Compositions (Based on Hooks and Forks)

A verb is produced by trains of three or two verbs, as defined by the following diagrams:
           FORK                 HOOK 
        g        g           g       g
       / \      / \         / \     / \
      f   h    f   h       y   h   x   h
      |   |   / \ / \          |       |
      y   y   x y x y          y       y
For example, 5(+*-)3 ↔ (5+3)*(5-3) .

The foregoing definition is from Section II F of the dictionary. The following examples concern functions used in statistics:
   mean=: +/%#                              Mean
   norm=: ] - +/ % #                        Centered on mean
   sqcm=: 2: ^~ ] - +/ % #                  Sqr of centred on mean
   var =: [:    mean 2: ^~ ] - mean=: +/%#  Variance
   stdv=: 2:%:[:mean 2: ^~ ] - mean=: +/%#  Standard Deviation

   ,.&.>@(];mean;norm;sqcm;var;stdv) y=: 2 3 4 5
+-+---+----+----+----+-------+
|2|3.5|_1.5|2.25|1.25|1.11803|
|3|   |_0.5|0.25|    |       |
|4|   | 0.5|0.25|    |       |
|5|   | 1.5|2.25|    |       |
+-+---+----+----+----+-------+
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