Hi David,

GaussianFilter is a standard smoothing method for data lists. Its the discrete version of smoothing a function with a moving average produced by the convolution of a piecewise continuous function with a Gaussian kernel ~ Exp[-x^2/sigma] of the normal distributiion.

Smoothing an Interpolation With a Gaussian Filter

This is a noisy data set from x|->(x/3)^2 Sin[2[Pi] x/22].

noisyf =  
  Array[({#, (#/3.0)^2 Sin[2 \[Pi] #/22] + 3.5 #  RandomReal[] } &), {56}, 0];

ListPlot[noisyf  ]

The data set is smoothed

 smoothf[s_]:= 
  smoothf[s] = 
(Transpose[  {#[[1]],  GaussianFilter[#[[2]], s] }] &)[Transpose[noisyf]];

Manipulate[
 Show[{ ListPlot[noisyf  , PlotStyle -> {Red, Opacity[0.5]},  Joined -> True], 
   ListPlot[smoothf[n], PlotStyle -> {Blue}, Joined -> True]}],
 {n,   Range[0, 7, 0.5]}]

Regards Roland

Please provide your efforts in the form of the Wolfram Language code. This will make it easier for other members to help you. Check several methods available to include your code in the rules http://wolfr.am/READ-1ST