Standard Deviation manipulation

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I am studying statistics and I feel as though I have a decent grasp on the subject but I am struggling with one concept (which is quite important), Standard Deviation. I understand that Standard Deviation is seeing how close your data points are to the mean of your data. I know that if it is "Normal" it should make a bell curve and I know the 68%, 95% and 99% rule.

My question is, is there a way to lower the standard deviation of your already plotted data set? Ideally when testing some sort of Hypothesis you would want it to fall within the Mean (or within + or - 1 STD). If it falls outside 1 STD then it is Statistically insignificant to which you need to look into "why" in much further detail.

I am not sure if this falls within more of a data science question because you are trying to manipulate data but any help or insight would be greatly appreciated!

Thanks!