Page 69 - Statistics for Dummies

Chapter 4: Tools of the Trade

The standard deviation is also used to describe where most of the data should
fall, in a relative sense, compared to the average. For example, if your data
have the form of a bell-shaped curve (also known as a normal distribution),
about 95% of the data lie within two standard deviations of the mean. (This
result is called the empirical rule, or the 68–95–99.7% rule. See Chapter 5 for
more on this.)
The standard deviation is an important statistic, but it is often absent when
statistical results are reported. Without it, you’re getting only part of the story
about the data. Statisticians like to tell the story about the man who had one
foot in a bucket of ice water and the other foot in a bucket of boiling water.
He said on average he felt just great! But think about the variability in the two
temperatures for each of his feet. Closer to home, the average house price, for
example, tells you nothing about the range of house prices you may encounter
when house-hunting. The average salary may not fully represent what’s really
going on in your company, if the salaries are extremely spread out.
Don’t be satisfied with finding out only the average — be sure to ask for the 53
standard deviation as well. Without a standard deviation, you have no way of
knowing how spread out the values may be. (If you’re talking starting salaries,
for example, this could be very important!)
Percentile
You’ve probably heard references to percentiles before. If you’ve taken any
kind of standardized test, you know that when your score was reported, it
was presented to you with a measure of where you stood compared to the
other people who took the test. This comparison measure was most likely
reported to you in terms of a percentile. The percentile reported for a given
score is the percentage of values in the data set that fall below that certain
score. For example, if your score was reported to be at the 90th percentile,
that means that 90% of the other people who took the test with you scored
lower than you did (and 10% scored higher than you did). The median is right
in the middle of a data set, so it represents the 50th percentile. For more spe-
cifics on percentiles, see Chapter 5.
Percentiles are used in a variety of ways for comparison purposes and to
determine relative standing (that is, how an individual data value compares to
the rest of the group). Babies’ weights are often reported in terms of percen-
tiles, for example. Percentiles are also used by companies to see where they
stand compared to other companies in terms of sales, profits, customer satis-
faction, and so on.

3/25/11 8:17 PM
08_9780470911082-ch04.indd 53 3/25/11 8:17 PM
08_9780470911082-ch04.indd 53