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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
http://mathforum.org/dr.math/
```
Associated Topics:
High School Statistics

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