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Part II: Number-Crunching Basics
Measuring Relative Standing
with Percentiles
Sometimes the precise values of the mean, median, and standard deviation
just don’t matter, and all you are interested in is where you stand compared
to the rest of the herd. In this situation, you need a statistic that reports rela-
tive standing, and that statistic is called a percentile. The k percentile is a
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number in the data set that splits the data into two pieces: The lower piece
contains k percent of the data, and the upper piece contains the rest of the
data (which amounts to [100 – k] percent, because the total amount of data is
100%). Note: k is any number between 1 and 100.
The median is the 50th percentile: The point in the data where 50% of the data

fall below that point, and 50% fall above it.
In this section, you find out how to calculate, interpret, and put together per-
centiles to help you uncover the story behind a data set.
Calculating percentiles
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To calculate the k percentile (where k is any number between one and one
hundred), do the following steps:
1. Order all the numbers in the data set from smallest to largest.
2. Multiply k percent times the total number of numbers, n.
3a. If your result from Step 2 is a whole number, go to Step 4. If the result
from Step 2 is not a whole number, round it up to the nearest whole
number and go to Step 3b.
3b. Count the numbers in your data set from left to right (from the small-
est to the largest number) until you reach the value indicated by Step
3a. The corresponding value in your data set is the k percentile.
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4. Count the numbers in your data set from left to right until you reach the
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one indicated by Step 2. The k percentile is the average of that corre-
sponding value in your data set and the value that directly follows it.
For example, suppose you have 25 test scores, and in order from lowest to
highest they look like this: 43, 54, 56, 61, 62, 66, 68, 69, 69, 70, 71, 72, 77, 78,
79, 85, 87, 88, 89, 93, 95, 96, 98, 99, 99. To find the 90th percentile for these
(ordered) scores, start by multiplying 90% times the total number of scores,
which gives 90% ∗ 25 = 0.90 ∗ 25 = 22.5. Rounding up to the nearest whole
number, you get 23.

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