Question

A sample of 26 offshore oil workers took part in a simu- lated escape exercise, resulting in the accompanying data on time (sec) to complete the escape "Oxygen Consumption and Ventilation During Escape from an Offshore Platform," Ergonomics, 1997: 281-292): 36. 389 356 359 363 375 424 325 394 402 373 373 370 364 366 364 325 339 393 392 369 374 359 356 403 334 397 a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare?

Answer 1

Solution:

a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare?

Answer:

The display is reasonably symmetric, so the mean and median will be close.

b. Calculate the values of the sample mean and median.

Answer: The sample mean is given below:

$\boldsymbol{\bar{x}=\frac{\sum x}{n}=\frac{9638}{26}=370.69 sec.}$

To find the median, we need to sort the data in ascending order as:

$325,325,334,339,356,356,359,359,363,364,$

$364,366,369,370,373,373,374,375,389,$

$392,393,394,397,402,403,424$

Since the number of observations is even, therefore, the median is the average of the middle two numbers.

$\boldsymbol{Median=\frac{369+370}{2}=369.5 sec.}$

c. By how much could the largest time, currently, 424, be increased without affecting the value of the sample median?

Answer: We know that the median is not affected by extreme values, therefore, 424 can be increased by any value and doing so will not affect the value of the sample median.

By how much could this value be decreased without affecting the value of the sample median?

Answer: 424 could be decreased to 370 and doing so will not affect the value of the sample median.

d. What are the values of $\bar{x}$ and $\tilde{x}$ when the observations are reexpressed in minutes?

Answer: The value of the sample mean will be:

$\boldsymbol{\bar{x}=\frac{370.69}{60}=6.18 min.}$

and the value of the sample mean will be:

$\boldsymbol{\tilde{x}=\frac{369.5}{60}=6.16 min.}$