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Standard Deviation and Units

Date: 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 
Associated Topics:
High School Statistics

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