Make a box-and-whisker plot for each data set. Area in 1,000 mi2 of 13 western states. 122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77 median: __________ lower quartile: ________ upper quartile: _________

To find the median, you must first order the data values from least to greatest:
71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164
The median is the middle value so the median is 98.
The lower quartile is the median of the first half of the data. The first half of the data does not include the median of the set so the first half of the data is:
71, 71, 77, 84, 85, 98
Since the first half of the data has an even number of values, the median of the first half is the average of the two middle values of 77 and 84. The median is then $\frac{77+84}{2}=80.5$ so the lower quartile is 80.5.
The upper quartile is the median of the second half of the data. The second half of the data does not include the median of the set so the second half of the data is:
104, 111, 114, 122, 147, 164
Since the second half of the data has an even number of values, the median of the second half is the average of the two middle values of 114 and 122. The median is then ${\displaystyle \frac{(114+122)}{2}=118}$ so the upper quartile is 118.
To make the box-and-whisker plot, plot the minimum of 71, the lower quartile of 80.5, the median of 98, the upper quartile of 118, and the maximum of 164. Draw a box that has sides at the lower and upper quartiles. Draw a vertical segment in the box passing through the median. Then draw segments from the minimum to the lower quartile and from the upper quartile to the maximum:
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