251y0451 10/20/04 ECO251 QBA1 FIRST HOUR EXAMOctober 6, 2004 Name: _____KEY______________ Student Number : _____________________ Class Hour: _____________________ Remember – Neatness, or at least legibility, counts. In most non-multiple-choice questions an answer needs a calculation or short explanation to count.Part I. (7 points)Use the eleven numbers that you used in the second problem in the take-home exam. (If you don’t have them – take your student number plus the numbers (3, 6, 9, 9, 21) . Example: Seymour Butz’s student number is 876509, so he gets 8, 7, 6, 5, 0, 9, 3, 6, 9, 9, 21. Of course, he has read “Things That You Should Never Do on an Exam or Anywhere Else” and knows that he can’t use them this way. ) Compute the following:a) The Median (1)b) The Standard Deviation (3)c) The 2nd Quintile (2)d) The Coefficient of variation (1)Solution: Seymour used the eleven numbers 1, 3, 12, 15, 22, 7, 7, 5, 2, 10, 1 . The numbers in order are 1, 1, 2, 3, 5, 7, 7, 10, 12, 15, 22. x 2x1x 1 1 2x 1 13x 2 44x 3 95x 5 256x 7 497x 7 498x 10 1009x 12 14410x 15 22511x 22 484Total 85 1091a) The middle number is 7.b) ,11n 72727.71185nxx, 1072727.711109112222nxnxs41818.4310181818.434. So 589247.641818.43 sc) 124.1 npposition=4.8. So 4a and 8.. b.)(.11 aaapxxbxx so 6.4358.38.4546.4.1xxxxxd) 8527.072727.7589247.6xsC1251y0451 10/20/04If you enjoy wasting time, you might want to use the definitional formula. x xx 2xx 1x 1 -6.7273 45.2562x 1 -6.7273 45.2563x 2 -5.7273 32.8024x 3 -4.7273 22.3475x 5 -2.7273 7.4386x 7 -0.7273 0.5297x 7 -0.7273 0.5298x 10 2.2727 5.1659x 12 4.2727 18.25610x 15 7.2727 52.87311x 22 14.2727 203.711Total 85 0.0003 434.182,11n 72727.71185nxx, 122nxxs 4182.4310182.434. The vast majority of people who thought that they were using the definitional formula used 12nxx, which, I believe, should have given them 2x. Doing a little bit of homework should have prevented this error.2251y0451 10/07/04Part II.1. The problem in the textbook that gives the data used in the take home also gives the braking distance for a sample of domestic made cars. It is presented below. Cumulative frequency (in red)is needed to get the median and was not given.Distance(feet) frequency Cumulative frequency 210 - 220 1 1 220 - 230 1 2 230 – 240 1 3 240 – 250 1 4 250 – 260 4 8 260 - 270 3 11 270 - 280 6 17 280 - 290 4 21 290 - 300 2 23 300 – 310 2 25 310 - 320 0 25 Sum 25 Minitab was used to calculate statistics from these data. It claims the following: (Note!!!!!),269x ,5252s .61.72813k You will not be able to use any of these numbers in b) orc) without some manipulation in parts b and c. Answers below are not acceptable unless you give some evidence in the sample statistics.a) Do American cars have a shorter braking distance? Compare all 3 measures of central tendency. (2)b) Are American cars more consistent in braking distance than foreign cars? Use a dimension-free measurement of variability. (2)c) Compare the direction and degree of skewness in the two distributions. Use one dimension- free measure of skewness. (2)d) Write a 5-number summary of the results from the first take-home problem. (2) 15Solution: a) Seymour had given us, for the foreign-made cars. 647.260x,6810.2555.5.1xx and the mode is 255. For the median for the domestic cars 13265.1 npposition. Since 13 is above 11 and below 17, the median is in 270-280, which has a frequency of 6. 5.27210611255.2705.5.1xx. The mode is the midpoint of the largest group, which is 275.Domestic ForeignMean 269 260.647Median 272.5 255.681Mode 275 255According to all measures, American cars have a longer braking distance.b) Seymour says for the foreign cars 8271.23731.567 s. If we compute the coefficient of variation, sxC Domestic 08518.269913.22C Foreign 0914.647.2608271.23C. American cars are more consistent.3251y0451 10/07/04c) You can use 1g or SK Domestic ForeignMean 269 260.647Mode 275 2553k -7281.61 8389.92 s 22.913 23.8271331skg 6053.913.2261.72813 38271.2393.8689= .6424or deviationstdmodemeanSK.3 786.913.222752693 711.0.8271.23255647.2603My answers are not consistent. 1g makes Foreign more skewed, while SK makes Domestic look moreskewed. However, Domestic is skewed to the left and Foreign to the right. d) Lower Limit 210First Quartile 243.5Median 255.681Third Quartile 275.357Upper Limit 3202. The following numbers refer to miles-per-gallon of a sample of vehicles (Bowerman and O’Connell).Class (mpg) f relf F relF29.8 - 30.3 ____ ____ ____ .061230.4 – 30.9 ____ ____ ____ .244931.0 – 31.5 ____ ____ 24 ____ 31.6 – 32.1 ____ .2653 35 .755132.2 – 32.7 11 .2245 46 .938832.8 – 33.3 3 .0612 49 1.000 Fill in the missing numbers. (5) 20Even with corrections made above, this had some errors, but I still could check easily to see if you knew what you were doing. The completely corrected results were.Class (mpg) f relf F relF29.8 - 30.3 3 .0612 3 .061230.4 – 30.9 9 .1837 12 .244931.0 – 31.5 12 .2449 24 .4898 31.6 – 32.1 13 .2653 37 .755132.2 – 32.7 9 .1837 46 .938832.8 – 33.3 3 .0612 49 1.000Total 49 1.00004251y0451 10/07/04Part III. (At least 22 points – 2 points each unless marked)1. Mark the variables below as qualitative (A) or quantitative (B)a) Number of days a patient stays at a spa Bb) Preferences for 10 beers on a 1st to 10th scale Ac) Method of contraception Ad) Per cent change in population between censuses B2. Which of the following is an example of continuous ratio data?a) Number of days a patient stays at a spab) Preferences for beers on a 1 to 10 scalec) Method of contraceptiond) *Per cent change in population between censusese) None of the above. 43. A
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