### MATHEMATICS 150

#### 2001/2002

PROBLEM SET 1

Solutions are due on Thursday, October 11. Solutions may be submitted in class or may be delivered by 4:00 pm to the instructor's office.

1. In part of a small sample survey on students in one program, fifteen students selected at random reported their anticipated total education-related debt by the time of graduation to the nearest hundred dollars. The sample amounts (re-expressed in thousands of dollars) were as follows.

 12.4 24.8 13.6 15.8 12.3 16.7 14.3 5.9 8.3 13.6 7.6 11.6 11.8 19.6 21.7
a) List the data in order from smallest to largest and illustrate the data with a dot diagram.
b) Display these data with stem-and-leaf display.
c) Display these data with a box-and-whisker plot.
2. A sampling of 88 blue boxes produced the following weights of wine, spirits and beer glass (in grams)

 3003 0 2436 1970 0 5820 397 2785 0 0 0 0 6345 338 0 0 0 211 442 469 1329 0 0 0 418 0 723 0 0 0 0 1396 642 700 0 0 391 685 303 507 4303 653 535 0 0 3835 149 356 0 511 0 0 0 2643 50 583 194 10889 256 381 0 723 585 0 7570 538 1129 664 210 0 0 5004 0 62 0 433 3424 0 366 4392 4314 0 642 0 949 0 525 0
Note: If you wish to analyze these data with computer software, they are available at
http://euclid.trentu.ca/math/courses/stat/files/glass.dat

 Convert the data set as follows. Delete all cases in which there was no glass (value =0). Convert all other values to kilograms rounded to the nearest tenth, rounding 5's up. (Eg, 3835 should be changed to 3.835 and then rounded to 3.8 and 50 should be changed to 0.05 and then rounded to 0.1.)
a) Display the converted data set with a stem-and-leaf display with stem labels 0, 1, 2, 3, etc. (include a multiplication code, if appropriate.)
b) Summarize the converted data with a frequency distribution based on the stem-and-leaf display.

3. For the converted data set in Problem 2, determine the following. (Use the individual converted values NOT the summary from Problem 2 b).)

a) median
b) first and third quartiles
c) 10th and 90th percentiles

4. Illustrate the converted data set in Problem 2 with a box-and-whisker plot.

5. In order to determine the appropriate "flat-rate" to charge for a particular type of repair, a service centre operator had staff perform the repair several times to become familiar with the process and then do the same type of repair another set of times (mixed in with other, different repairs to match usual conditions) to determine a "benchmark". Collectively, the staff had 75 sample benchmark times. These sample times produced the following frequency distribution of times in minutes (overleaf.) Determine the median, the 10th and the 90th percentiles for these data.

 Sample Benchmark Repair Times
 Repair Time (Minutes) 50 - 54 55 - 59 60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89 90 - 94 Number of Cases 2 6 5 19 10 8 7 5 3

6. A customer survey involved investigating criteria that customers consider important for gas stations, including reasons for switching. Consider a subsample including only customers who had switched companies. The subsample produced the following numbers of customers giving each of the stated reasons as the most important reason for having switched from each of two companies. Combine the data for both companies into one data set and then use a Pareto diagram based on percentages to illustrate the combined data.

 Numbers of Customers Switching from Gas Companies
 Reason Given as Most Important Price of Gas Location  Other Companies' Promotions Quality of Service Other Companies' Features Such as Convenience Store Other Company A 31 17 6 3 2 3 Company B 19 8 14 8 2 4

7. For the data in Problem 1, determine the following:

a) mean
b) range
c) mean deviation
d) variance (Use the defining formula and show the related work.)
e) standard deviation
f) coefficient of variation

8. For the converted data set in Problem 2, determine the following: (Use the individual converted values NOT the summary from Problem 2 b).)

a) mean
b) range
c) variance (Use the calculating formula or a function key on a calculator or computer software.)
d) standard deviation (Use the calculating formula or a function key on a calculator or computer software.)
e) coefficient of variation

9. A Canadian Government report on wage settlements in June 1999 listed five agreements in public administration. The reported numbers of employees involved and the average annual base rate increases were as listed below. Determine the overall mean base rate increase.

 Agreement Number of Employees Average Annual Base Rate Increase (%) A  1400 2.5 B 3200 1.5 C 1950 3.0 D 550 2.2 E 7600 6.0

10. The total annual enrolments over all courses in an academic program over a five-year period were 837, 891, 954, 1041, and 1093.

a) What was the percentage year-over-year change from the second year to the third?
b) What was the total percentage change from the first year to the fifth.
c) What was the average percentage year-over-year change?

### PROTOCOL FOR MATH 150 PROBLEM SET SOLUTION SUBMISSION

TRENT MATH
 E.A. Maxwell   2001-09-15