Sample 14. Compositions II

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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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