# 7.12: Applications of Box-and-Whisker Plots

**Basic**Created by: CK-12

**Practice**Applications of Box-and-Whisker Plots

Suppose you survey 1500 students in three counties and collect the number of brothers and sisters each one has. How would you represent this data? What tools would you use to organize this data? How would you find the median number of siblings?

### Watch This

First watch this video to learn about creating box-and-whisker plots with a calculator.

CK-12 Foundation: Chapter7ApplicationsofBoxandWhiskerPlotsA

Then watch this video to see some examples.

CK-12 Foundation: Chapter7ApplicationsofBoxandWhiskerPlotsB

### Guidance

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.

#### Example A

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.

#### Example B

List the five-number summary values for the data in Example A.

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:

#### Example C

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.

### Vocabulary

The ** TRACE feature** of a TI-83 calculator gives the individual values of the five-number summary of a data set one at a time when used with a box-and-whisker plot.

### Guided Practice

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?

**Answer:**

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.

### Interactive Practice

### Practice

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.

### Image Attributions

Here you'll learn how to use Texas Instruments calculators to create box-and-whisker plots and to determine the five-number summary of a data set.