We want to determine whether we can find the measures of spread and center we identified in Part A. Let's do it!

Mean of the Top Box Plot

To find the mean of the top box plot, we would have to sum of all of the data values and then divide it by the number of values in the data set. We do not know all the data values or the number of the values in the set. As such, we cannot find the mean for the top box plot.

Mean Absolute Deviation of the Top Box Plot

The mean absolute deviation of a data set is the average of the difference between the data values and the mean. We already determined that we cannot find the mean of the data set, which means that we also cannot find the mean absolute deviation for the top box plot.

Median of the Bottom Box Plot

The median is a measure of center that lies in the middle of a data set when the data set is written in numerical order. Recall that a box plot consists of three parts: a box and two whiskers.

The left whisker extends from the minimum to the first quartile.
The box extends from the first to the third quartile and has a vertical line through the median.
The right whisker extends from the third quartile to the maximum.

Now, take another look at the bottom box plot.

We can see that the box plot has a vertical line through the median. This means that we can find the median for the bottom box plot.

Interquartile Range of the Bottom Box Plot

The interquartile range is the difference between the upper quartile $Q_{3}$ and the lower quartile $Q_{1} .$ Let's find the quartiles of the bottom box plot!

We can see that $Q_{1}$ is $8$ and $Q_{3}$ is $24 .$ This means that we can calculate the interquartile range for the bottom box plot.

Exercise

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