SimpleHistogram[thisData_]:=Manipulate[thisMean=N[Mean[Select[thisData,#1≥rangemin&&#1≤rangemax&]]];thisSigma=N[StandardDeviation[Select[thisData,#1≥rangemin&&#1≤rangemax&]]];
thisLength=N[Length[Select[thisData,#1≥rangemin&&#1≤rangemax&]]];Show[Histogram[thisData,{rangemin,rangemax,width},PlotLabel->"N="<>ToString[NumberForm[N[thisLength],0,NumberPoint->""]]<>", mean="<>ToString[NumberForm[N[thisMean],3]]<>",  sigma="<>ToString[NumberForm[N[thisSigma],3]],AxesLabel->{"data value","counts per bin"}],Plot[(thisLength width E^(-((x-thisMean)^2/(2 thisSigma^2))))/Sqrt[2 π thisSigma^2],{x,rangemin,rangemax},PlotRange->All]],{{rangemin,Min[thisData]-0.2 (Max[thisData]-Min[thisData]),Minimum},Min[thisData]-0.2 (Max[thisData]-Min[thisData]),Max[thisData]+0.2 (Max[thisData]-Min[thisData])},{{rangemax,Max[thisData]+0.2 (Max[thisData]-Min[thisData]),Maximum},Min[thisData]-0.2 (Max[thisData]-Min[thisData]),Max[thisData]+0.2 (Max[thisData]-Min[thisData])},{{width,N[1/10 (Max[thisData]-Min[thisData])],Bin width},1/300 (Max[thisData]-Min[thisData]),Max[thisData]-Min[thisData]},ControlType->{InputField,InputField,InputField}]

t={};Do[AppendTo[t,Mean[RandomVariate[DiscreteUniformDistribution[{0,1}],100]]],{n,10000}]; SimpleHistogram[t]