A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape: $$\begin{array} { l l l l l l l l }
373 & 370 & 364 & 366 & 364 & 325 & 339 & 393 \
356 & 359 & 363 & 375 & 424 & 325 & 394 & 402 \
392 & 369 & 374 & 359 & 356 & 403 & 334 & 397
\end{array}$$
a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare?
b. Calculate the values of the sample mean and median.
c. By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample mean?
d. What are the values of $\bar { x }$
and $\tilde { x }$
when the observations are re-expressed in minutes?

Question

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape: $$\begin{array} { l l l l l l l l } 
373 & 370 & 364 & 366 & 364 & 325 & 339 & 393 \
356 & 359 & 363 & 375 & 424 & 325 & 394 & 402 \
392 & 369 & 374 & 359 & 356 & 403 & 334 & 397
\end{array}$$ 
a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare?
b. Calculate the values of the sample mean and median.
c. By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample mean?
d. What are the values of $\bar { x }$ 
and $\tilde { x }$ 
when the observations are re-expressed in minutes?

Quizplus · Accepted Answer

The Answer is a. A. stem-and-leaf display of this data appears below:

\begin{array} { l l l } 32 & 55 & ext { stem: ones } \33 & 49 & ext { leaf: tenths } \34 & & \35 & 6699 & \36 & 34469 & \37 & 03345 & \38 & 9 & \39 & 2347 & \40 & 23 & \41 & & \42 & 4 &\end{array}

$a. A. stem-and-leaf display of this data appears below: \begin{array} { l l l } 32 & 55 & ext { stem: ones } \ 33 & 49 & ext { leaf: tenths } \ 34 & & \ 35 & 6699 & \ 36 & 34469 & \ 37 & 03345 & \ 38 & 9 & \ 39 & 2347 & \ 40 & 23 & \ 41 & & \ 42 & 4 & \end{array} The display is reasonably symmetric, so the mean and median will be close. b. The sample mean is \bar { x } = 9638/26 = 370.7. The sample median is ilde { x } = (369+370)/2=369.50. c. The largest value (currently 424) could be increased by any amount. Doing so will not change the fact that the middle two observations are 369 and 170, and hence, the median will not change. However, the value x = 424 can not be changed to a number less than 370 ( a change of 424-370 = 54) since that will lower the values(s) of the two middle observations. d. Expressed in minutes, the mean is (370.7 sec)/(60 sec) = 6.18 min; the median 6.16 min.$ The display is reasonably symmetric, so the mean and median will be close.
b. The sample mean is

\bar { x }

= 9638/26 = 370.7. The sample median is

ilde { x }

= (369+370)/2=369.50.
c. The largest value (currently 424) could be increased by any amount. Doing so will not change the fact that the middle two observations are 369 and 170, and hence, the median will not change. However, the value x = 424 can not be changed to a number less than 370 ( a change of 424-370 = 54) since that will lower the values(s) of the two middle observations.
d. Expressed in minutes, the mean is (370.7 sec)/(60 sec) = 6.18 min; the median 6.16 min.

A Sample of 26 Offshore Oil Workers Took Part in a Simulated