Chapter 11, Problem 10CST

i.

To determine

To make a box-and-whisker plot

Answer to Problem 10CST

The box-and-whisker plot for Rachel’s is:

  

The box-and-whisker plot for Vivian’s is:

  

Explanation of Solution

Given:

Rachel’s $60$ meter dash times (in seconds) : $9.82,10.35,9.75,9.91,10.04,9.87$

Vivian’s $60$ meter dash times (in seconds) : $9.79,10.24,10.08,9.73,9.81,9.85$

Calculation:

Arrange Rachel’s $60$ meter dash times (in seconds) in ascending order:

  $9.75,9.82,9.87,9.91,10.04,10.35$

Lower extreme $=9.75$

Lower quartile $=9.82$

Median $=9.89$

Upper quartile $=10.04$

Upper extreme $=10.35$

The box-and-whisker plot for Rachel’s is:

  

Arrange Vivian’s $60$ meter dash times (in seconds) in ascending order:

  $9.73,9.79,9.81,9.85,10.08,10.24$

Lower extreme $=9.73$

Lower quartile $=9.79$

Median $=9.83$

Upper quartile $=10.08$

Upper extreme $=10.24$

The box-and-whisker plot for Vivian’s is:

  

ii.

To determine

To compare the medians and ranges.

Answer to Problem 10CST

The median for Vivian’s $60$ meter dash times is better than Rachel’s $60$ meter dash times, since Vivian take less time to complete the $60$ meter dash.

The range of Vivian’s $60$ meter dash times is less than Rachel’s $60$ meter dash times.

Explanation of Solution

Given:

Rachel’s $60$ meter dash times (in seconds) : $9.82,10.35,9.75,9.91,10.04,9.87$

Vivian’s $60$ meter dash times (in seconds) : $9.79,10.24,10.08,9.73,9.81,9.85$

Calculation:

The median for Rachel’s $60$ meter dash times (in seconds) $9.89$

The median forVivian’s $60$ meter dash times (in seconds) $9.83$

Therefore,

The median for Vivian’s $60$ meter dash times is better than Rachel’s $60$ meter dash times, since Vivian take less time to complete the $60$ meter dash.

The range of Rachel’s $60$ meter dash times (in seconds) $=10.35-9.75=0.60$

The range of Vivian’s $60$ meter dash times (in seconds) $=10.24-9.73=0.51$

Therefore,

The range of Vivian’s $60$ meter dash times is less than Rachel’s $60$ meter dash times.

iii.

To determine

To find which one is faster.

Answer to Problem 10CST

Vivian is faster than Rachel..

Explanation of Solution

Given:

Rachel’s $60$ meter dash times (in seconds) : $9.82,10.35,9.75,9.91,10.04,9.87$

Vivian’s $60$ meter dash times (in seconds) : $9.79,10.24,10.08,9.73,9.81,9.85$

Vivian’s median value is $9.83$ seconds and Rachel median value is $9.89$ seconds.

It shows that Vivian took less time to complete the $60$ meter dash as compared to Rachel.

Hence,

Vivian is faster than Rachel.