Healthy fast food? Refer to Exercise 102. Find the interquartile range of the fat content distribution shown in the dotplot.

The given dot plots are:

The data value of the given dot-plot are:

8, 12, 15, 17, 21, 22, 26, 27, 27, 29, 31, 40

Interquartile range:

$IQR=Q_3-Q_1$

As the number of data, values is even, and the median is the average of the sorted data set's two middle values (6th and 7th data values):

$$\begin{gathered} M=Q_2=\frac{22+26}{2} \\ =\frac{48}{2} \\ =24 \end{gathered}$$

The median of data values below the median (or at 25% of the data) is the first quartile. The first quartile is the average of the 3rd and 4th data values because there are 6 data values below the median.

$$\begin{gathered} Q_1=\frac{15+17}{2} \\ =\frac{32}{2} \\ =16 \end{gathered}$$

The median of the data values above the median (or at 75% of the data) is the third quartile. The third quartile is the average of the 9th and 10th data values since there are 6 data values above the median.

$$\begin{gathered} Q_3=\frac{27+29}{2} \\ =\frac{56}{2} \\ =28 \\ IQR=28-16 \\ =12 \end{gathered}$$

The interquartile range is 12 grams.