Page 103 - Statistics for Dummies

Chapter 5: Means, Medians, and More
The percentiles for 2007 are all higher than the percentiles for 2001 (which
is a good thing!). They are also more spread out. For 2007, the difference
between the 20th and 50th percentiles is around $30,000, and from the 50th
to the 80th it’s approximately $50,000; both of these differences are larger
than for 2001. Similarly, the 10th percentile is farther from the 50th (about
$38,000 difference) in 2007 compared to 2001, and the 50th is farther from the
90th (by about $86,000) in 2007, compared to 2001.These results tell us that
incomes are increasing in general at all levels between 2001 and 2007, but
the gap is widening between those levels. For example, the 10th percentile
for income in 2001 was $10,913 (as seen in Table 5-3), compared to $12,162
in 2007; this represents about an 11 percent increase (subtract the two and
divide by 10,913). Now compare the 95th percentiles for 2007 versus 2001;
the increase is almost 18%. Now, technically, you may want to adjust the 2001
values for inflation, but you get the basic idea.
Percentage changes affect the variability in a data set. For example, when
salary raises are given on a percentage basis, the diversity in the salaries
also increases; it’s the “rich get richer” idea. The guy making $30,000 gets a 87
10 percent raise and his salary goes up to $33,000 (an increase of $3,000); but
the guy making $300,000 gets a 10 percent raise and now makes $330,000 (a
difference of $30,000). So when you first get hired for a new job, negotiate the
highest possible salary you can because your raises that follow will also net a
higher amount.
Examining ACT Scores
Each year millions of U.S. high school students take a nationally administered
ACT exam as part of the process of applying for colleges. The test is designed
to assess college readiness in the areas of English, Math, Reading, and
Science. Each test has a possible score of 36 points.
ACT does not release the average or standard deviation of the test scores
for a given exam. (That would be a real hassle if they did, because these sta-
tistics can change from exam to exam, and people would complain that this
exam was harder than that exam when the actual scores are not relevant.)
To avoid these issues, and for other reasons, ACT reports test results using
percentiles.
Percentiles are usually reported in the form of a predetermined list. For
example, the U.S. Census Bureau reports the 10th, 20th, 50th, 80th, 90th, and
95th percentiles for household income (as shown in Table 5-3). However,
ACT uses percentiles in a different way. Rather than reporting the exam
scores corresponding to a premade list of percentiles, they list each possible
exam score and report its corresponding percentile, whatever that turns out
to be. That way, to find out where you stand, you just look up your score and
you’ll find out your percentile.

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