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	352	354	360	379	423	324	397	402
374	375	370	362	366	366	327	339	394
390	369	377	357	354	407	330	397

(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	1
33	2
34	3
35	4
36	5
37	6
38	7
39	8
40	9
41	10
42	11

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 median will be greater than the mean.     The display is reasonably symmetric, so the mean and median will be close. The display is positively skewed, so the median will be greater than the mean. The display is negatively skewed, so the mean will be greater than the median.

(b) Calculate the values of the sample mean x and median x . [Hint: Σx_i = 9628.] (Round your answers to two decimal places.)

x =	13 sec
x =	14 sec

(c) By how much could the largest time, currently 423, be increased without affecting the value of the sample median? (Enter ∞ 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.)

x	= 17 min
x	= 18 min

Answer 1

(a)

Following is the stem-and-leaf display of the data:

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

(b)

Following table shows the sum of data values and ordered data set:

	X
	324
	327
	330
	339
	352
	354
	354
	357
	360
	362
	366
	366
	369
	370
	374
	375
	377
	379
	383
	390
	394
	397
	397
	402
	407
	423
Total	9628

The mean is

Median: Since there are 26 data values so median will be average of 13th and 14th data values. So median is

(c)

Median is the middle value of ordered data set. So largest value can be increased to infinity.

It can be decreased upto 370 because below it order of data values will be changed.

(d)

The mean in minutes is

The median is