Question

##########################################################################################
# Use R to create a stemplot
# Copy the data and code below
# Run the code in R

time=c(	383,	350,	354,	360,	379,	421,	321,	396,	403,	372,	375,	372,	363,
	368,	365,	328,	336,	395,	390,	369,	378,	359,	352,	409,	334,	399)
stem(time,1)

#Note: If your stems from R are not the same as below. Change 1 in the stem function to 2.

########################################################################################## code if needed

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: # Use R to create a stemplot # Copy the data and code below Run the code in R time-c383, 350, 354, 360, 379, 421, 321, 396, 403, 372, 375, 372, 363, 368, 365, 328, 336, 395, 390, 369, 378, 359, 352, 409, 334, 399) stem(time,1) # Note: If your stems from R are not the same as below. Change 1 in the stem function to 2 (a) Construct a stepot in R af 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 41 42 How does it suggest that the sample mean and median will compare? 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 negatively skewed, so the mean will be greater than the median The display is positively skewed, so the median will be greater than the mean The display is positively skewed, so the mean will be greater than the median (b) Calculate the values of the sample mean x and medianX. (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 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 ㏄ if there is no limit to the amount.) (d) What are the values of x and ? when the observations are reexpressed in minutes? (Round your answers to two decimal places.) min min

Answer 1

(a) The stem and leaf plot is given below:
32 | 1846
33 | NONE
34 | 0249
35 | NONE
36 | 0358922589
37 | NONE
38 | 30569
39 | NONE
40 | 39
41 | NONE
42 | 1

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

(b) sample mean=370.42, sample median=370.50

(c) By how much the value of 421 can be decreased = 421 - 372 = 49.
By how much the value be increased = $\infty$ (infinity)

(d) sample mean=6.17, sample median=6.18