Question

File sizes Refer to Exercises 101 and 105. Identify any outliers in the distribution. Show your work.

Short answer

There are no outliers.

Step-by-step solution

Step 1. Given information.

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.

The first quartile is 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 14th data value since there are 9 data values above the median.

The third quartile is 4.7.

Interquartile range is 2.8 megabyte.

Step 3. Identify any outliers in the distribution.

Observations that are more than 1.5 times the IQR above or below Q1 are considered outliers.

$$\begin{gathered} Q_3+1.5IQR=4.7+1.5\left(2.8\right) \\ =8.9 \\ {Q}_1-1.5IQR=1.9-1.5\left(2.8\right) \\ =-2.3 \end{gathered}$$

Because all of the data values are within $-2.3and8.9$, there are no outliers.