284 Part 4: The State of the World
Interquartile Range
The interquartile range, or IQR, is similar to the range, as you can tell from its name. The other
part of the name, interquartile, means between the quartiles. To find the range, you subtract the
minimum value from the maximum value. To find the interquartile range, you subtract the first
quartile from the third quartile (Q3 – Q1).
Look back at the data about number of books read that you used to find quartiles.
Number of books read last year: 16, 23, 13, 24, 25, 16, 17, 28, 19, 14, 12, 22, 13, 24, 15, 26, 27, 18, 29
This data set has a minimum of 12 and a maximum of 29, for a range of 17. You found Q1 = 15,
median = 19, and Q3 = 25. The interquartile range is Q3 – Q1 = 25 – 15 = 10.
The reason you sometimes want to use the interquartile range instead of the range is that the
very high and very low values in your data often straggle far away from the other data. That
exaggerates the range. The IQR cuts off those straggly parts but still gives you a sense of the
spread.Standard Deviation
The third commonly used measure of spread is the one that’s more complicated to find. It’s
called the standard deviation, and like the range and the IQR, the bigger it is, the more spread
out the data are. The standard deviation tells you how much the other numbers in the data
set vary from the average. For this reason, it is often paired up with the mean; for example,
you might hear that a data set has a mean of 42 with a standard deviation of 3. A low standard
deviation tells you that the numbers in the data set are close to the mean, while a high standard
deviation indicates that the numbers in a data set are far from the mean.
Understanding the standard deviation is harder than understanding the range, but here’s a way to
think about what the mean and standard deviation tell you.
The mean tells you how to locate the center of the data set.
The IQR tells you where the middle 50 percent of the data is.
The range tells you where 100 percent of the data is.
The standard deviation breaks the range up into sections, letting you gauge how far from the
mean another value is.
The standard deviation is like a ruler, measuring how from the center a value falls.
So what is the standard deviation? The deviation part refers to how far from the mean each
number in the data set is. That’s the simple piece. The standard part refers to the more
complicated work that’s done to avoid or eliminate things that could confuse the information.