Q48. - Algebra 1

Question

The results for an annual 5K race are shown at the right. Make a box-and-whisker plot for the data. Write a sentence describing what the length of the box-and-whisker plot tells about the times for the race. (Lesson 0-13)

Annual 5K Race Results
Joe	14:48	Carissa	19:58
Jessica	19:27	Jordan	14:58
Lupe	15:06	Taylor	20:47
Dante	20:39	Mi-Ling	15:48
Tia	15:54	Winona	21:35
Amber	20:49	Angel	16:10
Amanda	16:30	Catalina	20:21

Step-by-Step Solution

Answer

The upper and lower quartile are $14:48$ and $21:35$.

Step 1. Write down the given data.

The given data is shown below.

Annual 5K Race Results
Joe	14:48	Carissa	19:58
Jessica	19:27	Jordan	14:58
Lupe	15:06	Taylor	20:47
Dante	20:39	Mi-Ling	15:48
Tia	15:54	Winona	21:35
Amber	20:49	Angel	16:10
Amanda	16:30	Catalina	20:21

Step 2. Arrange the given data from least to greatest.

Arrange the data in order from least to greatest.

$\begin{array}{l}14:48,14:58,15:48,16:10,16:30.19:27,19:58,20:21,\\ 20:39,20:47,20:49,21:35\end{array}$

Step 3. Evaluate upper and lower quartile.

Calculate the lower quartile.

$\begin{array}{l}\frac{\left(16:30+19:27\right)}{2}=\frac{35:57}{2}\\ =15:48\end{array}$

Again, calculate the upper quartile.

$20:39$

The smallest number is $14:48$.

The largest number is $21:35$.

The length of the box and whisker plot gives the range of times which varied between $14:48$ and $21:35$.

Therefore, the upper and lower quartile are $14:48$ and $21:35$.