Correcting smoothed data

CFAI curriculum “one heuristic approach to correcting for smoothed data is to rescale the data in such a way that their dispersion is increased but the mean of the data is unchanged.” Then this is further explained in Example 8 in Reading 16.

Could someone please explain the above…i dont seem to get it. I understand the problem of smoothed data but i dont understand the idea of “increasing dispersion whilst keeping hte mean unchanged”.

what is smoothing doing? reducing peaks and valleys - so the data looks smooth.

To unsmooth - keep the mean the same - (center line remains the same) - but increase peaks and valleys. So it now increases the dispersion - thus unsmoothing the data.

thanks CPK