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 388 350 354 361 379 423 322 395 402 373 375 372 362 367 365 327 335 393 392 368 377 357 352 405 333 399 (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 34 35 36 37 38 39 40 42 How does it suggest that the sample mean and median will compare? The display is positively skewed, so the mean will be greater than the median The display is negatively skewed, so the mean will be greater than the median The display is reasonably symmetric, so the mean and median will be close The display is negatively skewed, so the median will be greater than the mean The display is positively skewed, so the median will be greater than the mean (b) Calculate the values of the sample mean x and median . [Hint: Ex 9626.] (Round your answers to two decimal places.) sec sec (c) By how much could the largest time, currently 423, be increased without affecting the value of the sample median? (Enter oo 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 co if there is no limit to the amount.)

Answer 1

Solution

Stems	Leaves
32	2,7
33	3,5
34	-
35	0,2,4,7
36	1,2,5,7,8
37	2,3,5,7,9
38	8
39	2,3,5,9
40	2,5
41	-
42	3

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

(b) mean = 9626/26 = 370.23 sec

median = 372 (n/2+1 = 14th)

(c) infinity i.e. no limit as median is not affected by the extreme items

infinity (same reason)