Statistics

This calculates the mean and the standard deviation of data represented by values (Xs) and their frequencies (Ns).

test_statistics:-
  Xs = [3.7, 3.8, 3.9, 4.0, 4.1, 4.2, 4.3],
  Ns = [  1,   3,   5,   9,   8,   3,   1],
  statistics(Ns, Xs,         Mean, StdVarPopulation, StdVarSample),
  fwrite(f, 10, 2, Mean),             % 4.01
  fwrite(f, 10, 7, StdVarPopulation), % 0.1350309
  fwrite(f, 10, 7, StdVarSample), nl. % 0.1373392

statistics(Ns, Xs, Mean, StdVarPopulation, StdVarSample):-
  statistics_1(Ns, Xs, 0, S_N, 0, S_NX, 0, S_NXX),
  Mean is S_NX / S_N,
  StdVarPopulation is sqrt((S_NXX - Mean * Mean * S_N) / S_N),
  StdVarSample is sqrt((S_NXX - Mean * Mean * S_N) / (S_N - 1)).

statistics_1([], [], S_N, S_N, S_NX, S_NX, S_NXX, S_NXX).
statistics_1([N|Ns], [X|Xs], S_N0, S_N, S_NX0, S_NX, S_NXX0, S_NXX):-
  S_N1 is S_N0 + N,
  N_X is N * X,
  S_NX1 is S_NX0 + N_X,
  S_NXX1 is S_NXX0 + N_X * X,
  statistics_1(Ns, Xs, S_N1, S_N, S_NX1, S_NX, S_NXX1, S_NXX).

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