data = Table[Table[{x,0.01+0.01*Sin[x/2.5]+RandomReal[NormalDistribution[0.,0.001]]},{x,1400,1401,0.03}],{100}];

meanval = Map[Mean,data][[All,2]];

StandardDeviation[meanval]

data5 = Table[Table[{x,0.01+0.01*Sin[x/2.5]+RandomReal[NormalDistribution[0.,0.001]]},{x,1400,1405,0.03}],{100}];

StandardDeviation[Map[Mean,data5][[All,2]]]

sig = Map[StandardDeviation,Table[Map[Mean,Table[Table[{x,1+0.01*Sin[x/0.5]+RandomReal[NormalDistribution[0.,0.005]]},{x,f,f+i,0.03}],{f,1400,1420,i}]][[All,2]],{i,1,10}]];

Show[ListPlot[sig,PlotMarkers->{Automatic,Medium}],Plot[sig[[1]]/Sqrt[x],{x,1,20},PlotRange->Full]]

ListPlot[Table[{x,1+0.01*Sin[x/0.5]+RandomReal[NormalDistribution[0.,0.005]]},{x,0,5,0.03}]]

sig = Table[{n,StandardDeviation[Map[Mean,Table[Table[{x,1+0.01*Sin[x/0.5]+RandomReal[NormalDistribution[0.,0.005]]},{x,i,i+n,0.03}],{i,0,100,n+0.03}]][[All,2]]]},{n,1,20,2}]

ListPlot[sig,PlotMarkers->{Automatic,Medium}]