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Chapter 2: Q92. (page 116)
In terms of percentiles, define QL, QM and QU
The QL is 25th percentile.
The QM is 50th percentile.
The QU is 75th percentile.
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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.
Calculate the range, variance, and standard deviation for the following samples:
a.4, 2, 1, 0, 1
b.1, 6, 2, 2, 3, 0, 3
c.8, -2, 1, 3, 5, 4, 4, 1, 3, 3
d.0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3,-2, -1, 0, 1
Question: Misleading graph.Consider the following graphic, similar to one produced by the Silicon Alley Insider, an online publication for business news. The graph attempts to show the increasing trend in annual revenue produced by Craigslist compared to the decrease in newspaper classified ad sales.
a.Why might the graph be misleading? [Hint:Focus on the units of measure on the two verticalaxes.]
b.Redraw the graph, but use the same units of measure for both Craigslist revenue and newspaper ad sales. What conclusions can you draw from the redrawn graph?
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.
Land purchase decision.A buyer for a lumber company must decide whether to buy a piece of land containing 5,000 pine trees. If 1,000 of the trees are at least 40 feet tall, the buyer will purchase the land; otherwise, he won鈥檛. The owner of the land reports that the height of the trees has a mean of 30 feet and a standard deviation of 3 feet. Based on this information, what is the buyer鈥檚 decision?
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