relative standard deviation
/ REL-uh-tiv STAN-derd dee-vee-AY-shun /
A wobble of one centimetre means almost nothing when you are measuring the length of a football field, but it is huge when you are measuring a pencil. The size of an error only makes sense next to the thing being measured. The relative standard deviation captures exactly that: it expresses the scatter as a fraction of the value, not as a raw amount.
The relative standard deviation is the standard deviation divided by the mean, usually written as a percentage. So a standard deviation of 0.1 around a mean of 100 gives an RSD of 0.1 percent, while the same 0.1 around a mean of 1 gives an RSD of 10 percent. It strips away the units and tells you, in plain proportional terms, how precise the measurement is for its size.
It matters because it lets you compare the precision of completely different measurements on a level playing field — micrograms against kilograms, one method against another. The caveat is that it becomes unstable and even meaningless as the mean approaches zero, because dividing by a tiny average blows the percentage up, so it should not be quoted for values near zero.
A method measuring 50.0 mg of drug with a standard deviation of 0.5 mg has an RSD of 1.0 percent. Many regulatory specifications demand an RSD below 2 percent for the result to be acceptable.
Spread expressed as a percentage of the value, ready for comparison.
Relative standard deviation and coefficient of variation are the same quantity under two names; coefficient of variation, or CV, is the term more common in biology and clinical work.