Mean, Median, and Variance Functions from Data 

Compute mean and other functions from processes or temporal data.

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X proc = WienerProcess[1, 1/2]; data = RandomFunction[proc, {0, 5, 0.1}, 25];

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X {Mean[proc[2.5]], Mean[data[2.5]]}

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Compare exact and estimated mean and standard deviation functions.

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X {Plot[{Mean[proc[t]], Mean[data[t]]}, {t, 0, 5}], Plot[{StandardDeviation[proc[t]], StandardDeviation[data[t]]}, {t, 0, 5}]}

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Combine with simulation data.

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X Show[ListLinePlot[data], Plot[{Mean[proc[t]] - 3 StandardDeviation[proc[t]], Mean[proc[t]] + 3 StandardDeviation[proc[t]]}, {t, 0, 5}, Filling -> {1 -> {2}}]]

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