251x0711 2/12/07
ECO251 QBA1
FIRST EXAM
February 21, 2007
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 IV. Do all the Following (12+ Points). These are based on problems by Edward J. Kane. Show your work!
1. In May 1997 Forbes Magazine provided data on the salaries of 50 CEOs. These were arranged by Allen
L. Webster to give the table below. Amounts are in thousands. Treat these data as a sample. Personalize the data below by adding the six digits of your student number to the last 6 frequencies. .For example,
Seymour Butz’s student number is 876509 so he adds 8 to second frequency and 7 to the third frequency, etc and uses {9, 19, 17, 14, 9, 3, and 14} (adding to 85). You may check your work on the computer, but what is turned in should look as if it had all been done by hand. a. Calculate the Cumulative Frequency (0.5)
Salary in Thousands Frequency b. Calculate the Mean (0.5)
1 90 to under 440 9
2 440 to under 790 11 c. Calculate the Median (1) d. Calculate the Mode (0.5)
3 790 to under 1140 10
4 1140 to under 1490 8
5 1490 to under 1840 4 e. Calculate the Variance (1.5) f. Calculate the Standard Deviation (1) g. Calculate the Interquartile Range (1.5)
6 1840 to under 2190 3
7 2190 to under 2540 5 h. Calculate a Statistic showing Skewness and interpret it (1.5) i. Make a frequency polygon of the data
(Neatness Counts!)(1) j. Extra credit: Put a (horizontal) box plot below the frequency chart using the same horizontal scale (1)
2. Take your student number as a sample of size 6. Each digit will be a separate number. Change all zeroes to nines. For example, Seymour Butz’s student number is 876509, so his numbers are 8, 7, 6, 5, 9 and 9. Find the following a) Geometric Mean b) Harmonic mean c) Root-mean-square
If you wish, d) Compute the geometric mean from a) using natural and/or base 10 logarithms. (1 point extra credit each).
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