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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