First Hour Exam s1

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ECO251 QBA1 FIRST HOUR EXAM October 6, 2004 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: 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)

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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]

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]

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]

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]

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]

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 ______

A2 and A3 ______

A2 , A3 , A4 ______

A1 and A3 ______[14]

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]

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Exhibit 1. The boxplot, stem-and-leaf display and 5 number summary describe the data set ‘Length’

Boxplot of Length

h 600 t g n e L 599

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 1.34

8. What are the median and the interquartile range for the data set in exhibit 1? [17]

9. Assume that you were asked to present these data in seven intervals, what class interval would you use? (Show your work!!!)

10. Show the intervals that you would actually use. [21] Class From to A B C D E F G 11. If we take the area between 602.75 and 597.39 a) According to the empirical rule, what percent of the data should be between these points? b) According to the Tchebyschev inequality, what percent of the data should be between these points? c) What percent of the data is actually between these points.? Comment. [27]

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Exhibit 2: class f f rel F Frel 0-10 .10 10-20 .30 20-30 .70 30-40 .20 40-50 .10 100 1.00 Total xxxx xxxx

12. Fill in the missing numbers in Exhibit 2. (4) [31]

13. Find the 61st percentile in exhibit 2.(3) [34]

14. An Economics course has students of all classes in it. 10% Freshmen, 46% sophomores, 30%Juniors and 14% Seniors. Make this information into a Pareto chart. (4) [38]

Extra Credit. I forwarded this to several people a few days ago. The headline appeared in a Slovak newspaper. The subject line is my comment. From what you know about ordinal data, write a short essay explaining my comment. I’m looking for your ability to express yourself persuasively as much as for facts.

Subject: A great example of the uselessness of ordinal data

Bratislava is the 44th most expensive city in the world

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Blank page for calculations.

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ECO251 QBA1 FIRST EXAM February 18, 2005 TAKE 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 III. Do all the Following (11 Points) Show your work!

1. The frequency distribution below represents mortgage payments in hundreds of dollars of 85 families to the Relatively Reliable Bank and Trust Company. Personalize the data below by adding the last digit of your student number to the last frequency and the second to last digit of your student number to the second to last digit,. For example, Seymour Butz’s student number is 876509 so he adds 0 to the second to last frequency and 9 to the last frequency and uses (1, 4, 18, 32, 16, 10, 0, 13).

Payment frequency a. Calculate the Cumulative Frequency (0.5) b. Calculate The Mean (0.5) 0 - 4 1 c. Calculate the Median (1) 4 - 8 4 d. Calculate the Mode (0.5) 8 – 12 18 e. Calculate the Variance (1.5) 12 – 16 32 f. Calculate the Standard Deviation (1) 16 – 20 16 g. Calculate the Interquartile Range (1.5) 20 – 24 10 h. Calculate a Statistic showing Skewness and 24 - 28 0 Interpret it (1.5) 28 - 32 4 i. Make a frequency polygon of the data showing relative or percentage frequency (Neatness Counts!)(1) j. Extra credit: Put a (horizontal) box plot below the relative frequency chart using the same scale. (1)

2. Take your student number followed by 10, 14, 16, 18, 20, 22 as 12 values of x . Change any zeros to ones. For example, Seymour Butz’s student number is 876509, so he uses 8, 7, 6, 5, 1, 9, 10, 14, 16, 18, 20, 22. For these eleven numbers, compute the a) Geometric Mean b) Harmonic mean, c) Root-mean-square (1point each). Label each clearly. If you wish, d) Compute the geometric mean using natural or base 10 logarithms. (1 point extra credit each ).