How to plot X and Y data to see average data converging?

Question

I initially have ran a large, say 1000 (to be changed later) number of monte carlo simulations (mcRun), and I want to see when the average data result starts to converge to a reasonable value.

So I basically first ran 1000 simulations, and took average data based on 0 to first 10%(100), then average data based on 0 to 20%(200) and so on. So just to show the data:

For[n = 0, n < 10, n++, Print [data[n]]]

{622.917} {583.165} {564.45} {570.583} {584.956} {583.185} {579.662} {572.974} {570.253} {558.536}

So how to plot this data where Y is data[0] to data[9] and X is 0.1 mcRun, 0.2mcRun...1 mcRun. Or possibly 3D animate later using Manipulate? as I will have more sensitivity analysis to be done later.

Answer 1

For example:

(*Dumbish MonteCarlo simm to calculate Pi*)
mcpi[n_Integer] :=  4 Total[Boole[Norm@# < 1] & /@ RandomReal[{-1, 1}, {n, 2}]]/n;
(*Use up to 10^8 points*)
ListLinePlot[
   Accumulate[mcpi /@ ConstantArray[#, #]] Array[1/# &, #],
   Epilog -> {Red, Thick, Dashed, Line[{{1, Pi}, {#, Pi}}]},
   AxesLabel -> {TraditionalForm[Sqrt[n]], ""}] &@10000