Page 68 - Statistics for Dummies

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Part I: Vital Statistics about Statistics
The mean may not be a fair representation of the data, because the average is
easily influenced by outliers (very small or large values in the data set that are
not typical).
Median
The median is another way to measure the center of a numerical data set.
A statistical median is much like the median of an interstate highway. On
many highways, the median is the middle, and an equal number of lanes lay
on either side of it. In a numerical data set, the median is the point at which
there are an equal number of data points whose values lie above and below
the median value. Thus, the median is truly the middle of the data set. See
Chapter 5 for more on the median.
The next time you hear an average reported, look to see whether the median
is also reported. If not, ask for it! The average and the median are two different
representations of the middle of a data set and can often give two very differ-
ent stories about the data, especially when the data set contains outliers (very
large or small numbers that are not typical).
Standard deviation
Have you heard anyone report that a certain result was found to be “two
standard deviations above the mean”? More and more, people want to report
how significant their results are, and the number of standard deviations
above or below average is one way to do it. But exactly what is a standard
deviation?
The standard deviation is a measurement statisticians use for the amount of
variability (or spread) among the numbers in a data set. As the term implies,
a standard deviation is a standard (or typical) amount of deviation (or dis-
tance) from the average (or mean, as statisticians like to call it). So the stan-
dard deviation, in very rough terms, is the average distance from the mean.
The formula for standard deviation (denoted by s) is as follows, where n
equals the number of values in the data set, each x represents a number in
the data set, and is the average of all the data:

For detailed instructions on calculating the standard deviation, see Chapter 5.

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