Page 102 - Statistics for Dummies

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Part II: Number-Crunching Basics
A percentile is not a percent; a percentile is a number (or the average of two

numbers) in the data set that marks a certain percentage of the way through
the data. Suppose your score on the GRE was reported to be the 80th percen-
tile. This doesn’t mean you scored 80% of the questions correctly. It means
that 80% of the students’ scores were lower than yours and 20% of the stu-
dents’ scores were higher than yours.
A high percentile doesn’t always constitute a good thing. For example, if your
city is at the 90th percentile in terms of crime rate compared to cities of the
same size, that means 90% of cities similar to yours have a crime rate that is
lower than yours, which is not good for you. Another example is golf scores;
a low score in golf is a good thing, so being at the 80th percentile with your
score wouldn’t qualify you for the PGA tour, let’s just say that.
Comparing household incomes
The U.S. government often reports percentiles among its data summaries. For
example, the U.S. Census Bureau reported the median (the 50th percentile)
household income for 2001 to be $42,228, and in 2007 it was reported to be
$50,233. The Bureau also reports various percentiles for household income
for each year, including the 10th, 20th, 50th, 80th, 90th, and 95th. Table 5-3
shows the values of each of these percentiles for both 2001 and 2007.
Table 5-3 U.S. Household Income (2001 versus 2007)
Percentile 2001 Household Income 2007 Household Income
10th $10,913 $12,162
20th $17,970 $20,291
50th $42,228 $50,233
80th $83,500 $100,000
90th $116,105 $136,000
95th $150,499 $177,000
Looking at the percentiles for 2001 in Table 5-3, you can see that the bottom
half of the incomes are closer together than the top half of the incomes are.
The difference between the 20th percentile and the 50th percentile is about
$24,000, whereas the spread between the 50th percentile and the 80th per-
centile is more like $41,000. The difference between the 10th and 50th percen-
tiles is only about $31,000, whereas the difference between the 50th and the
90th percentiles is a whopping $74,000.

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