Chapter 15.2, Problem 2WE

a.

To determine

Find the median.

Answer to Problem 2WE

  $78$

Explanation of Solution

Given information:

Given: The stem -and -leaf plot.

  $\begin{array}{ll}5\hfill & 9\hfill \\ 6\hfill & 3,3,7\hfill \\ 7\hfill & 1,6,6,6\hfill \\ 8\hfill & 0,0,4,4,8\hfill \\ 9\hfill & 2,5,5\hfill \end{array}$

Calculation:

Here, we have the data distribution of the given steam and leaf plot:

  $59,63,63,67,71,76,76,76,80,80,84,84,88,92,95,95$

Now, from the above distribution we can calculate our median:

  $\begin{array}{l}Median={\frac{n}{2}}^{th}and\frac{n}{2}+1^{th}terms\\ n=16\\ Median=\frac{16}{2}and\frac{16}{2}+1\\ Median=8^{th}and{9}^{th}terms\\ Median=\frac{76+80}{2}=78\end{array}$

Hence, the median is $78$ .

b.

To determine

Find the first quartile.

Answer to Problem 2WE

  $71$

Explanation of Solution

Given information:

Given: The stem and leaf plot.

  $\begin{array}{ll}5\hfill & 9\hfill \\ 6\hfill & 3,3,7\hfill \\ 7\hfill & 1,6,6,6\hfill \\ 8\hfill & 0,0,4,4,8\hfill \\ 9\hfill & 2,5,5\hfill \end{array}$

Calculation:

Here, the first quartile of the distribution means the median of the lower half of the given data.

Now, we have the lower half of the data:

  $59,63,63,67,71,76,76,76$

Hence, the first quartile for the given data is $71$ .

c.

To determine

Find the third quartile.

Answer to Problem 2WE

  $84$

Explanation of Solution

Given information:

Given: The stem and leaf plot.

  $\begin{array}{ll}5\hfill & 9\hfill \\ 6\hfill & 3,3,7\hfill \\ 7\hfill & 1,6,6,6\hfill \\ 8\hfill & 0,0,4,4,8\hfill \\ 9\hfill & 2,5,5\hfill \end{array}$

Calculation:

Here, the third quartile of the distribution means the median of the upper half of the given data.

Now, we have the upper half of the data:

  $80,80,84,84,88,92,95,95$

Hence, the first quartile for the given data is $84$ .

d.

To determine

Find the range.

Answer to Problem 2WE

  $36$

Explanation of Solution

Given information:

Given: The stem and leaf plot.

  $\begin{array}{ll}5\hfill & 9\hfill \\ 6\hfill & 3,3,7\hfill \\ 7\hfill & 1,6,6,6\hfill \\ 8\hfill & 0,0,4,4,8\hfill \\ 9\hfill & 2,5,5\hfill \end{array}$

Calculation:

Here, the range means the difference between the largest and smallest number given in the data.

Now we have $95$ as largest number and $59$ as smallest number. So, the difference will be:

  $95-59=36$

Hence, the range is $36$ .