Standard Deviation and UnitsDate: 04/02/2003 at 11:37:09 From: Brandon Subject: Standard deviation When calculating standard deviation of a data set with units of measure (i.e. centimeters, liters, etc.), is the calculated standard deviation a "unitless" value or does it include units of measure? For example: would the calculated standard deviation be reported as "0.35" or as "0.35 centimeters?" It seems to me that standard deviation would be a unitless value, but I repeatedly see people report it followed by inches, gallons or some other unit of measure. Date: 04/02/2003 at 13:13:41 From: Doctor Douglas Subject: Re: Standard deviation Hi, Brandon The standard deviation has the same units as the original data. For example, you could report the mean and standard deviation of a mass with any of the following: 102.2 kg +/- 13.6 kg 102.2 +/- 13.6 kg 102.2 (13.6) kg The variance has units of whatever the original data has, but squared (e.g. kg^2 for the above example). There is, however, a quantity that is unitless: the coefficient of variation (CV), which is simply the standard deviation divided by the mean. In the above example, the CV is (13.6 kg)/(102.2 kg) = 0.133. I hope this helps! - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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