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: 383 351 355 361 378 421 321 396 404 372 376 370 364 367 364 327 338395 393 369 378 357 353 406 333 399 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Stems Leaves 32 35 37 40 41 42 How does it suggest that the sample mean and median will compare? O The display is reasonably symmetric, so the mean and median will be close. O The display is positively skewed, so the mean will be greater than the median. O The display is positively skewed, so the median will be greater than the mean O The display is negatively skewed, so the mean will be greater than the median 0 The display is negatively skewed, so the median will be greater than the mean. (b) Calculate the values of the sample mean x and median X. [Hint: Σχ.-9631.] (Round your answers to two decimal places.) sec sec (c) By how much could the largest time, currently 421, be increased without affecting the value of the sample median? (Enter co if there is no limit to the amount By how much could this value be decreased without affecting the value of the sample median? (Enter if there is no limit to the amount.) (d) What are the values of x and X when the observations are reexpressed in minutes? (Round your answers to two decimal places.) min min

Answer 1

(a) The plot is given below:
32 | 1738
33 | NONE
34 | 1357
35 | NONE
36 | 1447902688
37 | NONE
38 | 33569
39 | NONE
40 | 46
41 | NONE
42 | 1

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

(b) sample mean = 370.42, median = 369.50

(c) By how much can it be increased? -> $\infty$
By how much can it be decreased? 51

(d) sample mean = 6.17, median = 6.16