Box-and-whisker plots – Practice Problems

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A box-and-whisker plot is a quick way of showing the variability of a data set. It displays the range and distribution of data along the number line.

To make a box-and-whisker plot, start by ordering the data from least to greatest. Next, inspect the ordered data set to determine these 5 critical values: minimum, Q1, median, Q3, and maximum and plot them above a number line.

The minimum and maximum values are the least and greatest values. The median or middle value splits the set of data into two equal numbered groups. The first quartile, Q1, is the median of the lower half of the data set. The third quartile, Q3, is the median of the upper half of the data set.

The box is created by drawing vertical line segments through Q1, median, and Q3 and drawing two horizontal line segments connecting the endpoints from Q1 to Q3 passing through the median. The first whisker is created by drawing a horizontal line connecting the minimum and Q1 while the second whisker is created by drawing a horizontal line connecting Q3 with the maximum.

A good measure of the spread of data is the interquartile range (IQR) or the difference between Q3 and Q1. This gives us the width of the box, as well. A small width means more consistent data values since it indicates less variation in the data or that data values are closer together.

Summarize and describe distributions.


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Exercises in this Practice Problem
Explain how to create a box-and-whisker plot.
Find the right box-and-whisker plot.
Compare the different data sets.
Find the data set(s) corresponding to the box-and-whisker plot pictured.
Label the values in a box-and-whisker plot.
Determine the interquartile range $(IQR)$.