Page 95 - Statistics for Dummies

deviation of the salaries for this team turns out to be $6,567,405; it’s almost
as large as the average. However, as you may guess, if you remove Kobe
Bryant’s salary from the data set, the standard deviation decreases because
the remaining salaries are more concentrated around the mean. The stan-
dard deviation becomes $4,671,508.
Watch for the units when determining whether a standard deviation is large.
For example, a standard deviation of 2 in units of years is equivalent to a
standard deviation of 24 in units of months. Also look at the value of the mean
when putting standard deviation into perspective. If the average number of
Internet newsgroups that a user posts to is 5.2 and the standard deviation is
3.4, that’s a lot of variation, relatively speaking. But if you’re talking about the
age of the newsgroup users where the mean is 25.6 years, that same standard
deviation of 3.4 would be comparatively smaller.
Understanding properties of standard deviation
Here are some properties that can help you when interpreting a standard
deviation: Chapter 5: Means, Medians, and More 79
✓ The standard deviation can never be a negative number, due to the way
it’s calculated and the fact that it measures a distance (distances are
never negative numbers).
✓ The smallest possible value for the standard deviation is 0, and that hap-
pens only in contrived situations where every single number in the data
set is exactly the same (no deviation).
✓ The standard deviation is affected by outliers (extremely low or
extremely high numbers in the data set). That’s because the standard
deviation is based on the distance from the mean. And remember, the
mean is also affected by outliers.
✓ The standard deviation has the same units as the original data.
Lobbying for standard deviation
The standard deviation is a commonly used statistic, but it doesn’t often get
the attention it deserves. Although the mean and median are out there in
common sight in the everyday media, you rarely see them accompanied by any
measure of how diverse that data set was, and so you are getting only part of
the story. In fact, you could be missing the most interesting part of the story.
Without standard deviation, you can’t get a handle on whether the data
are close to the average (as are the diameters of car parts that come off
of a conveyor belt when everything is operating correctly) or whether the
data are spread out over a wide range (as are house prices and income
levels in the U.S.).

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