Bratislava is the 44th most expensive city in the world251x0512 2/14/05ECO251 QBA1 FIRST HOUR EXAMFebruary 18, 2005 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)(Source: Prem S. Mann) The following numbers represent the price earnings ratio of 12 corporations.7, 16, 18, 18, 23, 21, 21, 19, 31, 34, 38, 58Compute the following:a) The Median (1)b) The Standard Deviation (3)c) The 61st percentile (2)d) The Coefficient of variation (1)Solution: The numbers in order are 7, 16, 18, 18, 19, 21, 21, 23, 31, 34, 38, 58..12n x 2x1x 7 492x 16 2563x 18 3244x 18 3245x 19 3616x 21 4417x 21 4418x 23 5299x 31 96110x 34 115611x 38 144412x 58 3364Total304 9650a) 65135.1 np The middle numbers are the 6th and 7th number, which are both 21. .2128750.xxxb) 3333.2512304nxx, 1123333.2512965012222nxnxs15336.177116869.1948. So3099.1315336.177 sc) 93.71361.1 np. So 7a and93.0. b)(.11 aaapxxbxx so)(93.078739.61.1xxxxx 86.22)2123(93.021 d) 5254.03333.253099.13xsC or 52.54%1251x0512 2/16/05How mean and variance were checked. The numbers were put into c1.————— 2/15/2005 10:44:12 PM ———————————————————— Welcome to Minitab, press F1 for help.————— 2/18/2005 3:53:24 PM ———————————————————— Welcome to Minitab, press F1 for help.MTB > let c2=c1*c1MTB > sum c1Sum of x Sum of x = 304MTB > sum c2Sum of xsq Sum of xsq = 9650MTB > describe c1;SUBC> mean;SUBC> variance;SUBC> stdev. Descriptive Statistics: x Variable Mean StDev Variancex 25.33 13.31 177.15MTB > print c1 c2Data Display Row x xsq 1 7 49 2 16 256 3 18 324 4 18 324 5 19 361 6 21 441 7 21 441 8 23 529 9 31 961 10 34 1156 11 38 1444 12 58 33642251x0512 2/16/05Part II. (At least 35 points – 2 points each unless marked - Parentheses give points on individual questions. Brackets give cumulative point total.)1. I have the average time of the first 10 runners in the Boston Marathon.a) Is this a parameter or a statistic? (Think!) b) What symbol should you use to indicate this mean? [2]Answer: This is a parameter, since the first 10 runners are a population – we have all of them. The symbol for a population mean is mu. 2. The data in question 1 is an example of a) Ordinal Datab) Nominal Datac) Discrete ratio datad) Continuous interval datae) *None of the above. [4]Answer: They are none of the above. Both the times of the runners and their average are continuous ratio data.3. Assume now that I have the times of all the runners who finish the Boston Marathon and that the first ten or 20 runners have times that are far below most of the rest, but that the more typical runners are relatively close together. Which of the following is most likely?a) *mean < median < modeb) mean < mode < medianc) mode < mean < mediand) mode < median < meane) none of the above. [6]Answer: The description (which might be highly inaccurate) is of a data set that is skewed to the left. The mean is the least robust of the measures of central tendency, so it will be pulled furthest to the right. The mode is the most robust and will hold its ground. The median is generally between them.4. Mark the variables below as qualitative (A) or quantitative (B)a) Celsius Temperatureb) Absolute Temperaturec) Cost of a new thermometerd) The number of thermometers you have in your house. [8]Answer: All of these variables are quantitative (B). The first is continuous interval data, the second and third are usually considered continuous ratio data and the last is discrete ratio data. 5. Which of the following is not a dimension – free measurement.a) *The population variance.b) Pearson’s measure of skewnessc)1gd) The coefficient of variation.e) The coefficient of excess.f) All of the above are dimension freeg) None of the above are dimension free. [10]Explanation: b – e are dimension-free ratios because they have data that are measured in thesame units in their numerators and denominators.3251x0512 2/16/056. Classify a deck of cards as follows: Write yes or no in each location.1A Hearts; 2A Red cards; 3A Black cards; 4A Face cards (4)Mutually Exclusive? Collectively Exhaustive?1A and 2A __no__ __no__2A and 3A __yes__ __yes_2A, 3A, 4A __no__ __yes_1A and 3A __yes__ __no__ [14]Explanation: 1A is inside 2A, and 2A hardly includes all cards. 2A and 3A do not overlap and between them include all cards. 4A includes parts of both 2A and 3A, but since2A and 3A already include all cards, the three classes are collectively exhaustive. Hearts cannot be black cards but 1A and 3A together leave out diamonds.7. What characteristic do the variance, standard deviation and Interquartile range have in common that they do not share with the mean, median, mode or skewness? (1)[15]Answer: They are all measures of dispersion.Exhibit 1. The boxplot, stem-and-leaf display and 5 number summary describe the data set ‘Length’Length602601600599598597Boxplot of Length4251x0512 2/16/05Exhibit 1. (ctd.) Stem-and-Leaf Display: Length (Numbers are in the 2nd and 3rd columns – 1st column is a form of cumulative count) 1 597 2 4 597 688 17 598 0000222224444 28 598 88888888888 41 599 0000022244444 44 599 666 49 600 00224(6) 600 668888 45 601 00000000002222222222224444444444444 10 601 666666888 1 602 2 Five number summary: Length Descriptive Statistics: Length 597.20 598.80 600.60 601.20 602.20 Mean 600.07 StDev 1.348. What are the median and the interquartile range for the data set in exhibit 1? [17]Solution: The mean is the middle number of the 5 number summary, 600.60. The IQR = Q3 – Q1 = 601.20 – 598.80 = 2.40.9. Assume that you were asked to present these data in seven intervals, what class interval would you use? (Show your work!!!) Solution: The highest number is 602.20 and the lowest is 597.20. 720.59720.602 w7143.. 0.8 is probably the smallest interval one could consider.10. Show the intervals that you would actually use. [21]Class From toA 597.0 597.7 B 597.8 598.5C
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