What is the difference between the standard deviation and relative standard deviation?

The standard deviation represents the square-root of the average squared difference between each datum and the mean. The relative standard deviation represents this as a percentage of the mean.

Take the dataset, ##X = {1, 1, 3, 5, 5}##, with standard deviation,

##sigma = sqrt((sum(X_i - barX)^2)/N) = 2##, and mean, ##mu = 3##.

To express this standard deviation as a percentage of the mean, we take the standard deviation over the mean (i.e., as a relative proportion), and multiply it by 100:

##sigma/abs(mu) xx 100 = 2/3 xx 100 ~~ 33.33%##

So, we can say the relative standard deviation,

##RSD = 3 +- 33.33%##