Question

File sizes Refer to Exercise 101. Find the interquartile range of the file size distribution shown in the dotplot.

Short answer

2.8 megabytes is the resultant answer.

Step-by-step solution

Step 1. Given information.

The given dot-plot is:

The data value of the given dot-plot are:

1.1, 1.3, 1.3, 1.6, 1.9, 1.9, 2.1, 2.2, 2.4, 2.5, 2.7, 3.0, 4.4, 4.7, 5.0, 5.6, 6.2, 7.5

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 (9th and 10th data values):

$$\begin{gathered} M=Q_2=\frac{2.4+2.5}{2} \\ =\frac{4.9}{2} \\ =2.45 \end{gathered}$$

The median of data values below the median (or at 25% of the data) is the first quartile. The first quartile is the 5th data value because there are 9 data values below the median.

$Q_1=1.9$

The median of the data values above the median (or at 75% of the data) is the third quartile. The third quartile is the $9+5=14th$data value since there are 9 data values above the median.

$Q_3=4.7$

$$\begin{gathered} IQR=4.7-1.9 \\ =2.8 \end{gathered}$$

Interquartile range is 2.8 megabyte.