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Chapter 2: Q38. (page 94)

Parking at a university has become a problem. The university鈥檚 administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 190 students and recorded how long it took each of them to find a parking spot. The durations had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 190 times collected.

Short Answer

Expert verified

Mean< Median

Step by step solution

01

Explaining the skewness toward left

The skewness shows the asymmetry and how distorted a variable is from the normal distribution. The variable could be skewed to the left or right.

02

Determining the relationship between mean and median

The researchers used observations to record the time it took for students to obtain the parking spot, and their findings indicate that the distribution was skewed toward the left. The relationship between mean and median is that the mean is lower than the median in this case as the distribution is skewed to the left.

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Most popular questions from this chapter

Ranking driving performance of professional golfers.A group of researchers developed a new method forranking the total driving performance of golfers on theProfessional Golf Association (PGA) tour (The Sport Journal,Winter 2007). The method requires knowinga golfer鈥檚 average driving distance (yards) and drivingaccuracy (percent of drives that land in the fairway).The values of these two variables are used to compute adriving performance index. Data for 40 PGA golfers (asranked by the new method for a recent tour year) aresaved in the accompanying file. The first five and last fiveobservations are listed in the table below.

a.Find the mean, median, and mode for the 40 driving performance index values.

b.Interpret each of the measures of central tendency, part a.

c.Use the results, part a,to make a statement about the type of skewness in the distribution of driving performance indexes. Support your statement with a graph.

Consider the following sample of five measurements: 2, 1, 1, 0, 3.

a.Calculate the range, s2, and s.

b.Add 3 to each measurement and repeat part a.

c.Subtract 4 from each measurement and repeat part a.

d.Considering your answers to parts a, b, and c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each measurement?

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.

Ranking driving performance of professional golfers.Refer to The Sport Journal(Winter 2007) analysis of anew method for ranking the total driving performance ofgolfers on the PGA tour, Exercise 2.52 (p. 97). Recall thatthe method uses both the average driving distance (yards)and driving accuracy (percent of drives that land in thefairway). Data on these two variables for the top 40 PGAgolfers are saved in the accompanying file. A professionalgolfer is practicing a new swing to increase his averagedriving distance. However, he is concerned that his drivingaccuracy will be lower. Is his concern a valid one? Explain.

Question: Corporate sustainability of CPA firms.Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 1.28 (p. 51). Corporate sustainability, recall, refers to business practices designed around social and environmental considerations. Data on the level of support for corporate sustainability were obtained for 992 senior managers. The level of support was measured quantitatively. The simulation was used to convert the data from the study to a scale ranging from 0 to 160 points, where higher point values indicate a higher level of support for sustainability.

a.A histogram for level of support for sustainability is shown next. What type of histogram is produced, frequency or relative frequency?

b.Use the graph to estimate the percentage of the 992 senior managers who reported a high (100 points or greater) level of support for corporate sustainability.
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