20160415_msd_improvement

data = Import["http://goo.gl/Fmm9fZ", "Table"][[1 ;; -2]];
dx = 1.9*10.^-3; data = data*dx;
meanDisp[data_, dn_] := Mean[Total[#^2] & /@ Differences[data, 1, dn]];
meanStd[data_, dn_] :=
  StandardDeviation[Total[#^2] & /@ Differences[data, 1, dn]];
meanXsq[data_, dn_] := Mean[#[[1]]^2 & /@ Differences[data, 1, dn]];
meanXsqStd[data_, dn_] :=
  StandardDeviation[#[[1]]^2 & /@ Differences[data, 1, dn]];
meanYsq[data_, dn_] := Mean[#[[2]]^2 & /@ Differences[data, 1, dn]];
meanYsqStd[data_, dn_] :=
  StandardDeviation[#[[2]]^2 & /@ Differences[data, 1, dn]];

{time, {msdMean, msdStdDev, xSquaredMean, xSquaredStdDev,
    ySquaredMean, ySquaredStdDev}} =
  AbsoluteTiming[
   Table[#[data, dn], {dn, 1, Length@data - 2}] & /@ {meanDisp,
     meanStd, meanXsq, meanXsqStd, meanYsq, meanYsqStd}];