Wiki Page, Math 13 - Perez Sandbox : Module 6 - Interquartile Range and Boxplots (2c of 3)

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2026-01-17T21:15:51-08:00

What a boxplot does not tell us

At this point, you should know how to

Create a boxplot from a five-number summary.

Use a boxplot to identify and interpret quartiles.

Identify the median and the IQR of a distribution from a boxplot.

Now we want to focus on what a boxplot does not tell us. A boxplot does not give us information about the following:

The number of data points in the data set.

The number of data points within each quartile (though each quartile contains the same number of data points).

The pattern of the data within each quartile.

EXAMPLE The same boxplots but very different distributions

Here are four data sets that illustrate these ideas.

How are these data sets similar? Notice that the four data sets have the same boxplot. This is because the five-number summary is the same for each data set. The data sets have identical minimum value, quartile marks and maximum value, so we can say that these data sets have the same center and spread.

Center: Each data set has a median of 10.

Spread: In each data set, the middle half of the data varies from 7 to 14, so the IQR is 7. In each data set, the data varies from 4 to 19, so the overall range is 15.

How are these data sets different? The data sets do not have the same number of data points. Also, the shape of each distribution is different. For small data sets, the boxplot does not give us reliable information about the shape.

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