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Errors by Significant Figures and Resolution

In the upper figure, average is 0.0400. And standard deviation is 0.0400. The lower figure uses the data rounded off to the first decimal place.

In the lower figure, standard deviation is 0.0518.

You may think that such small number of lower figure is not valid from the idea of significant figures. But standard deviation is useful to analyze the size of the dispersion of data.

In my experience, it is the general law that the standard deviation after the round off is larger than before.

If round off is done to the first decimal place the formulation is

"0.1" is from the stride of the data. "12" is from the formulation to calculate the standard deviation of uniform distribution.

This formulation may not be perfect. But it tells us the size of the effect of round off roughly.

NEXT Statistics with zero confidence interval (Impossibility of statistics)