Mathematica provides a package called “Hypothesis Testing” for analyzing random data. The package includes handy objects like “Around”, representing a quantity and the uncertainty around it. The following example code returns an Around object representing the confidence interval of the estimated bias of a coin after a repeated trial. As shown in the code, the ListPlot plots Around objects as such.

(*Load the Hypothesis Testing Package.*) Needs["HypothesisTesting`"]; coin[flips_, bias_] := (*Make the experiment and collect the data*) Module[{index, realizations, mean, conf, around}, realizations = {}; For[index = 1, index <= flips, index++, realizations = Append[realizations, RandomVariate[BernoulliDistribution[bias]]]; ]; (*Mean*) mean = Mean[realizations[[All]]]; (*Confidence interval*) conf = MeanCI[realizations[[All]]]; (*Around object*) around = Around[mean, Abs[conf[[1]] - conf[[2]]]] ] around = coin[1000, 0.5] ListPlot[{around}]

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