251x0611 2/10/06 ECO251 QBA1FIRST EXAMFebruary 16 and 17, 2006ECO251 QBA1 Name: _____________________ 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: Harvey J. Brightman) The following numbers are a sample and represent the pulse rates of 10 well-conditioned athletes.31, 33, 36, 37, 37, 47, 44, 41, 38, 39.Compute the following: Show your work!a) The Median (1)b) The Standard Deviation (3)c) The 31st percentile (2)d) The Coefficient of variation (1)1251x0611 2/10/06Part II. (At least 35 points – 2 points each unless marked - Parentheses give points on individual questions. Brackets give cumulative point total.) Exam is normed on 50 points.1. (Brightman) At an urban university, there are 7000 undergraduates whose ages are between 18 and 23, 2000 undergraduates between 24 and 29 years old, 1000 undergraduates between 30 and 35 years old and 1000 who are older than 35.a) Without doing any math, explain in plain English whether the mean will be below, the same as or above the median and why. (2) b) Where will the mode be relative to the mean and median? (1) [3] 2. I have the average time of 10 randomly picked runners in the Boston Marathon.a) Is this a parameter or a statistic? b) What symbol should you use to indicate this mean? [5]3. For a rather shapeless distribution with one mode, a mean of 100 and a standard deviation of 2, we can say that the percent of data falling between 80 and 120 isa) At least 90%b) At most 90%c) 100%d) At least 99%e) At most 99%f) None of the above. [7]4. For a mound-shaped (symmetrical) distribution with one mode, a mean of 100 and a standard deviation of 2, we can say that the percent of data falling above 96 isa) About 97.5%b) About 95%c) Almost 100%d) About 68%e) None of the above 5. The drawing of inferences about an unknown whole from a known part isa) Deductive reasoningb) Inductive reasoningc) Census takingd) Samplinge) None of the above. [11]6. Observations about a discrete quantitative variable a) Can be made in only two categoriesb) Can assume values only at specific points of a scale of values with inevitable gaps between these points.c) Can assume values at all points of a scale of values with no breaks in between possible values. d) Cannot be meaningfully multiplied or divided.e) Both b) and d) are true. [13] 7. Mark the variables below as qualitative or categorical (A), quantitative and continuous (B1) or quantitative and discrete (B2) (1 each)a) GPAb) Number of credits earnedc) Major area of studyd) Grade obtained in a statistics course. [17]8. If I double all of the incomes in a sample of 1000 people, mark below which of the statistics will change.a) Pearson’s measure of skewness2251x0611 2/10/06b) The coefficient of variation.c) The meand) All of the above will changee) None of the above will change . [19]TABLE 2-13Given below is the stem-and-leaf display representing the amount of detergent used in gallons (with leaves in 10ths of gallons) in a month by 25 drive-through car wash operations in Phoenix. (Ng p57) 9 | 14710 | 0223811 | 13556677712 | 22348913 | 029. In table 2-13, if a percentage histogram is constructed using 9.0 to 9.9 as the first class, what percent will be in the 12-12.9 class?[21]10. In table 2-13 find the median amount of detergent used. [23]11. Using the data in table 2-13. Assume that the data is to be presented in 6 classes, show how you would decide what class interval to use and list the classes below with their frequencies. (5) [28] Class FrequencyA __ to under __ __B __ to under __ __C __ to under __ __D __ to under __ __E __ to under __ __F __ to under __ __12. In Problem 3.42 in the text, data on waiting times in a bank in a commercial district is given. Assume that the 5-number summary is {0.38, 3.20, 4.50, 5.55, 10.03}. Use this to make a horizontal box plot, but first find the interquartile range. Then do the following: An upper fence is defined as Q3 + 1.5(IQR) and a lower fence is Q1 – 1.5(IQR). Indicate the fences by vertical lines at the end of the whiskers in your box plot – do not let the whiskers extend beyond the fences, but only show a fence if there is data beyond it. Any points beyond the fence should be represented by dots. (4)[32] 13. What characteristic do the mean, median and mode have that they do not share with the variance and the interquartile range? (1) [33]3251x0611 2/10/0614. The following data represents proven oil deposits in billions of barrels divided by region. Show this as a Pareto chart. (5)[37]Billions of Per Cent of Barrels TotalNorth America 54.8 5.3Central and South America 95.2 9.2Western Europe 17.2 1.7Africa 74.9 7.3Middle East 683.6 66.5Far East and Oceania 44.0 4.3Eastern Europe and CIS 59.0 5.74251x0611 2/10/06Blank page for calculations.5251x0611 2/10/06 ECO251 QBA1FIRST EXAMFebruary 16 and 17, 2006TAKE HOME SECTION Name: _________________________ Student Number: _________________________Throughout this exam show your work! Please indicate clearly what sections of the problem you are answering and what formulas you are using. Turn this is with your in-class exam. Part IV. Do all the Following (12+ Points). These are based on problems by Edward J. Kane. Show your work! 1. The following numbers give us the frequency distributions of interest rate changes in the US between 1801 and 1961 (153 years). Treat these data as a sample. Personalize the data below by adding the last digit of your student number to the first frequency and the second to last digit of your student number to the second frequency. For example, Seymour Butz’s student number is 876509 so he adds 9 to first frequency and 0 to the second frequency and uses {10, 2, 9, 25, 65, 35, 10, 5, and 1} (over 162 years). You may check your work on the computer, but what is turned in should look as if it had all been done by hand. Class Frequency -.95 to -.76 1-.75 to -.56 2-.55 to -.36 9-.35 to -.16 25 -.15 to .04 65 .05 to .24 35 .25 to .44 10 .45 to .64 5 .65 to .84 1 a. Calculate the Cumulative Frequency (0.5)b. Calculate the Mean (0.5)c. Calculate the Median (1)d.
View Full Document
Unlocking...