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Chapter 2: Q41E (page 94)
Describe how the mean compares to the median for distribution as follows:
a.Skewed to the left
b.Skewed to the right
c.Symmetric
a. The mean is smaller than the median
b. The mean is greater than the median
c. The mean and median are the same
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Question: The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 200 measurements are \(1,500 and \)300, respectively.
a.What are the units of measurement of the variable of interest? Based on the units, what type of data is this: quantitative or qualitative?
b.What can be said about the number of measurements between \(900 and \)2,100? Between \(600 and \)2,400? Between \(1,200 and \)1,800? Between \(1,500 and \)2,100?
Question: Repair and replacement costs of water pipes.Pipes used in a water distribution network are susceptible to breakage due to a variety of factors. When pipes break, engineers must decide whether to repair or replace the broken pipe.
A team of civil engineers estimated the ratio of repair to replacement cost of commercial pipe based on the diameter (in millimeters) of the pipe. (IHS Journal of Hydraulic Engineering,September 2012.) Data for a sample of 13 different pipe sizes are provided in the table. Use a scatterplot to aid the engineers in detecting a trend in the data. Does it appear that the ratio of repair to replacement cost is strongly associated with pipe size?
DIAMETER | RATIO |
80 | 6.58 |
100 | 6.97 |
125 | 7.39 |
150 | 7.61 |
200 | 7.78 |
250 | 7.92 |
300 | 8.20 |
350 | 8.42 |
400 | 8.60 |
450 | 8.97 |
500 | 9.31 |
600 | 9.47 |
700 | 9.72 |
Calculate the variance and standard deviation for samples where
a.n= 10, 鈭�x2 = 84, 鈭�x= 20
b.n= 40, 鈭�x2 = 380, 鈭�x= 100
c.n= 20, 鈭�x2 = 18, 鈭�x= 17.
Network server downtime.A manufacturer of network computer server systems is interested in improving its customer support services. As a first step, its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system downtime. The 40 most recent customers were surveyed to determine the amount of downtime (in hours) they had experienced during the previous month. These data are listed in the table.
Customer Number | Downtime | Customer Number | Downtime |
230 | 12 | 250 | 4 |
231 | 16 | 251 | 10 |
232 | 5 | 252 | 15 |
233 | 16 | 253 | 7 |
234 | 21 | 254 | 20 |
235 | 29 | 255 | 9 |
236 | 38 | 256 | 22 |
237 | 14 | 257 | 18 |
238 | 47 | 258 | 28 |
239 | 0 | 259 | 19 |
240 | 24 | 260 | 34 |
241 | 15 | 261 | 26 |
242 | 13 | 262 | 17 |
243 | 8 | 263 | 11 |
244 | 2 | 264 | 64 |
245 | 11 | 265 | 19 |
246 | 22 | 266 | 18 |
247 | 17 | 267 | 24 |
248 | 31 | 268 | 49 |
249 | 10 | 269 | 50 |
a.Construct a box plot for these data. Use the information reflected in the box plot to describe the frequency distribution of the data set. Your description should address central tendency, variation, and skewness.
b.Use your box plot to determine which customers are having unusually lengthy downtimes.
c.Find and interpret the z-scores associated with the customers you identified in part b.
Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.
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