251x0512 2 14 05 ECO251 QBA1 FIRST HOUR EXAM February 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 58 Compute 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 n 12 a p n 1 5 13 65 The middle x x2 numbers are the 6th and 7th number which are 7 49 x x8 x1 both 21 x 50 7 21 16 256 2 x 2 x 304 25 3333 x3 18 324 x4 x5 18 324 19 361 x6 21 441 x7 21 441 x8 23 529 x9 31 961 x10 34 1156 x11 x12 38 1444 c p n 1 61 13 7 93 So a 7 and b 0 93 x1 p x a b x a 1 x a so 58 3364 x1 61 x 39 x 7 0 93 x8 x 7 Total 304 9650 21 0 93 23 21 22 86 b x s2 n 12 2 x nx 2 n 1 9650 12 25 3333 2 12 1 1948 6869 177 15336 So 11 s 177 15336 13 3099 d C s 13 3099 0 5254 or 52 54 x 25 3333 1 251x0512 2 16 05 How 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 c1 MTB sum c1 Sum of x Sum of x 304 MTB sum c2 Sum of xsq Sum of xsq 9650 MTB SUBC SUBC SUBC describe c1 mean variance stdev Descriptive Statistics x Variable x Mean 25 33 StDev 13 31 Variance 177 15 MTB print c1 c2 Data Display Row 1 2 3 4 5 6 7 8 9 10 11 12 x 7 16 18 18 19 21 21 23 31 34 38 58 xsq 49 256 324 324 361 441 441 529 961 1156 1444 3364 2 251x0512 2 16 05 Part 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 Data b Nominal Data c Discrete ratio data d Continuous interval data e 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 mode b mean mode median c mode mean median d mode median mean e 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 Temperature b Absolute Temperature c Cost of a new thermometer d 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 skewness c g1 d The coefficient of variation e The coefficient of excess f All of the above are dimension free g None of the above are dimension free 10 Explanation b e are dimension free ratios because they have data that are measured in the same units in their numerators and denominators 3 251x0512 2 16 05 6 Classify a deck of cards as follows Write yes or no in each location A1 Hearts A2 Red cards A3 Black cards A4 Face cards 4 Mutually Exclusive Collectively Exhaustive A1 and A2 no no A2 and A3 yes A2 A3 A4 no A1 and A3 yes yes yes no 14 Explanation A1 is inside A2 and A2 hardly includes all cards A2 and A3 do not overlap and between them include all cards A4 includes parts of both A2 and A3 but since A2 and A3 already include all cards the three classes are collectively exhaustive Hearts cannot be black cards but A1 and A3 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 Boxplot of Length 602 Length 601 600 599 598 597 4 251x0512 2 16 05 Exhibit 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 4 597 17 598 28 598 41 599 44 599 49 600 6 600 45 601 10 601 1 602 2 688 0000222224444 88888888888 0000022244444 666 00224 668888 00000000002222222222224444444444444 666666888 2 Five number summary Length 597 20 598 80 600 60 601 20 Descriptive Statistics Length 602 20 Mean 600 07 StDev 1 34 8 What are the median and the interquartile range for the data set in exhibit 1 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 17 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 w 7143 0 8 is probably the smallest interval one could consider 602 20 597 20 7 10 Show the intervals that you would actually use Class A B C D E F G From 597 0 597 8 598 6 599 …
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