Chapter 13.3, Problem 7PPS

(a)

To determine

To Find:Median score of each room.

Answer to Problem 7PPS

Median for room $100$ is $94$

Median for room $110$ is $91$

Explanation of Solution

Given: The table shows the top score on a science test.

  

What is the median score of each room?

Arranging the data of both room in ascending order

We get

For room$100$

  $64,88,88,91,\underset{\_}{94},97,97,100,106$

Hence the median is $94$

For the room $110$

  $79,82,82,85,\underset{\_}{91},97,100,103,109$

Hence the median is $91$

(b)

To determine

To Find: The room which has greater range of score.

Answer to Problem 7PPS

Room $100$

Explanation of Solution

Given: The table shows the top score on a science test.

  

Which room has greater range of score?

For room$100$

Highest vale = $106$

Lowest value = $64$

Range = Highest value − lowest value

  $\begin{array}{l}=106-64\\ =42\end{array}$

For the room $110$

Highest vale = $109$

Lowest value = $79$

Range = Highest value − lowest value

  $\begin{array}{l}=109-79\\ =30\end{array}$

Hence, the room $100$ has greater range

(c)

To determine

To Find: The outlier in the data.

Answer to Problem 7PPS

Room $100$ has an outlier of $64$

Explanation of Solution

Given: The table shows the top score on a science test.

  

Of the top score shown, does either set of data have an outlier? If so, how does the outlier affect the range?

For room$100$

Median= $94$

Lower quartile = $88$

Upper quartile= $98.5$

Interquartile = $98.5-88=10.5$

Outlier

  $\begin{array}{l}10.5\times 1.5=15.75\\ 88-15.75=72.25\\ 98.5+15.5=114.25\end{array}$

Room $100$ has a range of $72.25-114.25$ and has an outlier of $64$ . This will affect the range of the data.

For the room $110$

Median= $91$

Lower quartile = $82$

Upper quartile= $101.5$

Interquartile = $101.5-82=19.5$

Outlier

  $\begin{array}{l}19.5\times 1.5=29.25\\ 82-29.25=52.25\\ 101.5+29.25=131.25\end{array}$

Room $110$ has a range of $52.25-131.25$ and hasno outlier.