### Applications of Box-and-Whisker Plots

The TI-83 or TI-84 can be used to create a box-and whisker plot. In the following examples, the TI-83 is used. In later Concepts, key strokes using the TI-84 will be presented to you. The five-number summary values can be determined by using the TRACE feature and the left and right arrows of the calculator or by pressing \begin{align*}\boxed{\text{STAT}}\end{align*} and using 1-Var Stats on the CALC menu. The **TRACE feature** gives the individual values of the five-number summary one at a time.

#### Using Technology to Construct a Box-and-Whisker Plot

The following numbers represent the number of siblings in each family for 15 randomly selected students:

\begin{align*}4, \ 1, \ 2, \ 2, \ 5, \ 3, \ 4, \ 2, \ 6, \ 4, \ 6, \ 1, \ 7, \ 8, \ 4\end{align*}

Use technology to construct a box-and-whisker plot to display the data.

A box-and-whisker plot can be created with a TI-83 calculator as shown below:

Note that when creating a box-and-whisker plot with a TI calculator, you don't have to actually sort the data. The calculator will sort the data automatically when creating the box-and-whisker plot.

#### Listing the Five-Number Summary

List the five-number summary values for the data in the previous example .

The five–number summary can be obtained from the calculator in 2 ways.

a. The following results are obtained by simply using the TRACE feature and the left and right arrows:

The values at the bottom of each screen are the five-number summary.

b. The second method involves pressing \begin{align*}\boxed{\text{STAT}}\end{align*} and using 1-Var Stats on the CALC menu for L1:

#### Constructing Box-and-Whisker Plots

Construct a box-and-whisker plot using technology to represent the average number of sick days used by 9 employees of a large industrial plant. The numbers of sick days are as follows:

\begin{align*}39 \quad 31 \quad 18 \quad 34 \quad 25 \quad 22 \quad 32 \quad 23 \quad 22\end{align*}

What are the values for the five-number summary?

The screens below show the five-number summary:

The values for the five-number summary are as follows:

Min. Value \begin{align*}\rightarrow 18\end{align*}

\begin{align*}Q_1 \rightarrow 22\end{align*}

Med \begin{align*}\rightarrow 25\end{align*}

\begin{align*}Q_3 \rightarrow 33\end{align*}

Max. Value \begin{align*}\rightarrow 39\end{align*}

This can be verified by pressing \begin{align*}\boxed{\text{STAT}}\end{align*} and using 1-Var Stats on the CALC menu for L1.

### Example

#### Example 1

The following data represents the number of flat-screen televisions assembled at a local electronics company for a sample of 28 days:

\begin{align*}& 48 \quad 55 \quad 51 \quad 44 \quad 59 \quad 49 \quad 47\\ & 45 \quad 51 \quad 56 \quad 50 \quad 57 \quad 53 \quad 55\\ & 47 \quad 49 \quad 51 \quad 54 \quad 56 \quad 54 \quad 47\\ & 50 \quad 53 \quad 52 \quad 55 \quad 51 \quad 59 \quad 48\end{align*}

Using technology, construct a box-and-whisker plot for the data. What are the values for the five-number summary?

First press \begin{align*}\boxed{\text{STAT}}\end{align*} and choose Edit on the EDIT menu. Enter the data values into L1, and then press \begin{align*}\boxed{\text{2ND}}\end{align*} \begin{align*}\boxed{\text{Y=}}\end{align*}. Press \begin{align*}\boxed{\text{ENTER}}\end{align*} and make sure that your settings are as follows. Note that for Type, the middle graph in the second row is selected.

Now press \begin{align*}\boxed{\text{WINDOW}}\end{align*} and make sure that your settings are as shown below:

Finally, press \begin{align*}\boxed{\text{GRAPH}}\end{align*}. The following screens show the steps necessary to determine the five-number summary using the TI-83:

The values for the five-number summary are as shown below:

Min. Value \begin{align*}\rightarrow 44\end{align*}

\begin{align*}Q_1 \rightarrow 48.5\end{align*}

Med \begin{align*}\rightarrow 51\end{align*}

\begin{align*}Q_3 \rightarrow 55\end{align*}

Max. Value \begin{align*}\rightarrow 59\end{align*}

This can be verified by pressing \begin{align*}\boxed{\text{STAT}}\end{align*} and using 1-Var Stats on the CALC menu for L1.

### Review

For each of the following box-and-whisker plots, determine the five-number summary and give one possible data set that could produce the box-and-whisker plot.

### Review (Answers)

To view the Review answers, open this PDF file and look for section 7.12.