We take tests throughout our school years and most of us understand how the scoring works. Take the number of points earned, divide by the number of points possible, move the decimal a couple of spaces right and, voila, we have a

*percent*that represents our score. (If you want to learn more about percents, there's a song for that.)

But then,
once a year, we take a standardized test and when the score is reported, we are
given a

*percentile*. What in the world is a percentile?
Unfortunately,
we don’t learn much about percentiles in school. However, we do learn about the median, which
I discussed in my

__last blog entry__, and also about quartiles. Let’s review briefly:
If all of
the values in a data set are arranged in order, then the middle number (or, if
there are two middle numbers, their average) is the

**. This number divides the data set into two equal groups: Half of the values in the set are above the median, and half of the values are below the median.***median*
If all of
the values in a data set are arranged in order, then the

**(there are three of them) are the values that split the data set into four equal groups:***quartiles*
One-fourth
(25%) of the values in the set are less than or equal to the 1

^{st}quartile, and three-fourths (75%) of the values are greater than or equal to the 1^{st}quartile.
Half (50%)
of the values in the set are less than or equal to the 2

^{nd}quartile, and half (50%) of the values are greater than or equal to the 2^{nd}quartile. (The 2^{nd}quartile is the same as the median.)
Three-fourths
(75%) of the values in the set are less than or equal to the 3

^{rd}quartile, and one-fourth (25%) of the values are greater than or equal to the 3^{rd}quartile.
If you
understand how quartiles work, then it’s not much of a leap to understand
percentiles.

If all of
the values in a data set are arranged in order, then the

**(there are 99 of them) are the values that split the data into 100 equal groups. (Note: some people call these***percentiles**centiles.*)
1% of the
values in the set are less than or equal to the 1

^{st}percentile, and 99% of the values are greater than or equal to the 1^{st}percentile.
2% of the
values in the set are less than or equal to the 2

^{nd}percentile, and 98% of the values are greater than or equal to the 2^{nd}percentile.
And so on…

Because they
split the data set into so many groups, percentiles are only useful in
analyzing data sets that are very large – like the number of students who take
standardized tests.

If we
understand how percentiles work, then interpreting standardized test scores
becomes much easier.

If a score
is reported as 20

^{th}percentile, then 20% of test-takers scored at or below that level.
If a score
is reported as 90

^{th}percentile, then 90% of test-takers scored at or below that level.
That wasn’t
so hard was it?

So, why are
there so many people who struggle with percentiles?

I blame
politicians.

In the recent years, politicians arguing over tax rates have consistently discussed “Americans in the top two percent of earners”. They would do us all a great service if they would instead argue about “Americans at or above the 98

^{th}percentile of earnings”. It wouldn’t make politicians any more likely to work well together, but at least people would understand standardized test scores better!

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