Chapter 20: Measures of Center and Spread 281The Separators
For small sets of data, you can take in the whole of the data set at once. The five test grades you
earned over the course of a semester probably don’t need to be broken up to help you understand
them. But for larger sets, especially for very large collections of data, being able to divide the list
up in organized ways can allow you to make comparisons that help you understand the important
information.
You might want to compare numbers within the data set, or you might want to make comparisons
between two related data sets. If a researcher was conducting a study on the cancer drugs, she
might want to compare the test results for two subjects in the same drug trial, perhaps to see if
gender or other factors changed the drug’s effectiveness, or she might want to compare the results
of the trials of two similar drugs to see which might be more effective.Quartiles and Percentiles
The most common ways of dividing up data sets are quartiles and percentiles. Quartiles divide
the data into four equal parts, or quarters. Percentiles divide the data into 100 equal parts.
Remember that percent means out of 100.
You could divide the data into any number of equal parts, and sometimes people do use other
“tiles.” Quintiles divide the data into five parts, for example. The quartiles and percentiles are
the most common ones, however.
Percentiles are most useful for very large data sets. It would be impossible to divide a data set
into 100 parts if it only contained 10 numbers. When there are hundreds or thousands of pieces
of information, like the scores for the SAT test administered all across the country, percentiles
can be a helpful way to compare values. If a score is at the 85th percentile, 85% of the scores are
below it and 15% are above. If your score was right in the middle of all scores, so that you were
at the median, you’d be at the 50th percentile. That means 50% of the scores are above you and
50%, or half, are below you.
For smaller sets of data, dividing into fewer parts makes more sense, and the most common is
four parts, called quartiles. The first quartile is the value that has one-fourth of the data below
it and three-fourths above. The second quartile has two-fourths, or half the data below and half
above. The second quartile is never called the second quartile, however, because it’s the median
and always gets that name. The third quartile has 75 percent of the data below and 25 percent
above. The first quartile, or Q1, the median, and the third quartile, Q3, divide the data set into
four equal parts.