Question

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

Short answer

12 grams is the resultant answer of interquartile range.

Step-by-step solution

Step 1. Given information.

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

Step 2. Find the interquartile range.

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.