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MATH 2565 (19)
Lecture

# PPS2_Solution_.doc

5 Pages
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School
York University
Department
Mathematics and Statistics
Course
MATH 2565
Professor
Jagmohan Chawla
Semester
Winter

Description
Problem4.13 a) The mean price of the electric smoothtop ranges is \$1001.50. b) In order to find the median and the quartiles, the list must be ordered. 565 750 850 900 1000 1050 1050 1200 1250 1400 The median price of the electric smoothtop ranges is \$1025. Quartile 1 = \$850 and Quartile 3 = \$1200. c) The range of the distribution of prices is Max – Min = \$1400 – \$565 = \$835. The IQR = Q3 – Q1 = \$1200 – \$850 = \$350. Problem4.15 a) As long as the boss’s true salary of \$200 000 is still above the median, the median will be correct. The mean will be too large, since the total of all the salaries will decrease by \$2 000 000 – \$200 000 = \$1 800 000, once the mistake is corrected. b) The range will likely be too large. The boss’s salary is probably the maximum, and a lower maximum would lead to a smaller range. The IQR will likely be unaffected, since the new maximum has no effect on the quartiles. The standard deviation will be too large, because the \$2 000 000 salary will have a large squared deviation from the mean. Problem 4.17 a) Set 2 has the greater standard deviation. Both sets have the same mean (6), but set two has values that are generally farther away from the mean. SD(Set 1) = 2.24 SD(Set 2) = 3.16 b) Set 2 has the greater standard deviation. Both sets have the same mean (15), maximum (20), and minimum (10), but 11 and 19 are farther from the mean than 14 and 16. SD(Set 1) = 3.61 SD(Set 2) = 4.53 c) The standard deviations are the same. Set 2 is simply Set 1 + 80. Although the measures of centre and position change, the spread is exactly the same. SD(Set 1) = 4.24 SD(Set 2) = 4.24 Problem 4.19 1200+700+6(400)+4(500)) a) The mean salary is 12 = 525 The median salary is the middle of the ordered list: 400 400 400 400 400 400 500 500 500 500 700 1200 The median is \$450. b) Only two employees, the supervisor and the inventory manager, earn more than the mean wage. c) The median better describes the wage of the typical worker. The mean is affected by the two higher salaries. d) The IQR is the better measure of spread for the payroll distribution. The standard deviation and the
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