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ECO251 QBA1
FIRST EXAM
February 21, 2007
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)
The following numbers are a sample and represent the prices of regular in a sample of 11 gas stations
2.28, 2.38, 2.50, 2.42, 2.34, 2.38, 2.44, 2.48, 2.38, 2.65, 2.66
Compute the following: Show your work!
a) The Median (1)
b) The Standard Deviation (3)
c) The 4th quintile (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.) Exam is normed on 50 points.
1. The difference between cumulative and ordinary frequency distributions is that the cumulative frequency
distribution shows the number of observations which are:
a) greater than particular values, whereas the ordinary frequency distribution shows the number of
observations in each class interval.
b) less than that particular values, whereas the ordinary frequency distribution shows the number
of observations in each class interval.
c) in each class interval less than that particular values, whereas the ordinary frequency
distribution shows the number of observations less than particular values.
d) in each class interval less than that particular values, whereas the ordinary frequency
distribution shows the number of observations greater than particular values.
e) none of the above.
2. Mark the variables below as qualitative or categorical (A), quantitative and continuous (B1) or
quantitative and discrete (B2) (1 each)
a) atmospheric pressure.
b) method of contraception
c) expenditure per pupil
d) Fahrenheit temperature.
e) Number of murders in Philadelphia over a year.
[7]
Exhibit 1: Given below is the stem-and-leaf display representing the amount of oil in gallons (with
leaves in gallons) used by a sample of 25 emergency generators during a power outage.
5
6
7
8
9
|
|
|
|
|
3.0
2.1
0.2
1.0
2.8
7.2
2.4
3.1
2.5
7.1
3.0 5.5 7.3 7.8 8.6 8.8 8.8
3.3 6.2 7.7 8.2 8.8
4.5 6.8
7.5
3. In Exhibit 1, if an ogive showing relative frequency is constructed using 50.0 to under 60.0 as the first
class, what will be the height of the point above 70 on the x axis?
[9]
4. In Exhibit 1 find the first quartile of amount of oil used.
[11]
5. Using the data in Exhibit 1, Assume that the data is to be presented in 7 classes, show how you would
decide what class interval to use and list the classes below with their frequencies. (5)
[16]
A
B
C
D
E
F
G
Class
__ to under __
__ to under __
__ to under __
__ to under __
__ to under __
__ to under __
__ to under __
Frequency
__
__
__
__
__
__
__
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6. If a frequency distribution is skewed to the left, which of the following measures is likely to have the
largest value?
[18]
a) mean
b) median
c) mode
d) All of the above will be almost the same size.
e) the parameter
f) It is impossible to tell unless we know whether we are dealing with a sample or a population.
7. A list of the countries that are members of the European Union in order of their GDP per capita is an
example of
[20]
a) Ordinal data.
b) Nominal data.
c) Interval data.
d) Ratio data.
e) None of the above.
8. A frequency distribution is of unknown shape and consists of 600 observations with a mean of 162 and a
standard deviation of 12.
a) What is the minimum number of observations that must fall between 138 and 186?
b) What is the maximum number of observations that could be above 210?
[24]
c) How would you change your answers to a) and b) if you found that the distribution was symmetrical and
unimodal? (3)
[27]
9. You have a deck of 52 cards consisting of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, king and queen of hearts,
clubs, diamonds and spades. Explain how you could divide the deck into 2 classes that are: (1 each)
a) collectively exhaustive but not mutually exclusive;
b) mutually exclusive but not collectively exhaustive;
c) both mutually exclusive and collectively exhaustive.
[30]
10. In ECO 252 you will learn to test a null hypothesis. A null hypothesis is a quantitative statement about
a population that can be disproved. The null hypothesis must meet three requirements: First, it must contain
 ,  or  ; Second, it must include a parameter or parameters and Third, it must contain reasonable values
for the parameter. Consider the following: (i)   3, (ii)   3, (iii) x  2, (iv) s  5, (v)   3.
The following could be null hypotheses:
a) (iii), (iv) and (v).
b) (i), (ii) and (v).
c) (i) and (ii).
d) (i) only.
e) all of the above
f) None of the above.
[32]
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11. Which of the following statements about the median is not true?
a) It is more affected by extreme values than the arithmetic mean.
b) It is a measure of central tendency
c) It is equal to the second quartile.
d) It is equal to the mode in symmetrical, unimodal distributions.
e) All of the above are true.
12. In a set of numerical data the second quartile is always halfway between the first and third quartile.
The above statement is: (1)
a) True
b) False
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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.
Salary in Thousands Frequency
1
2
3
4
5
6
7
90 to
440 to
790 to
1140 to
1490 to
1840 to
2190 to
under
under
under
under
under
under
under
440
790
1140
1490
1840
2190
2540
9
11
10
8
4
3
5
a. Calculate the Cumulative Frequency (0.5)
b. Calculate the Mean (0.5)
c. Calculate the Median (1)
d. Calculate the Mode (0.5)
e. Calculate the Variance (1.5)
f. Calculate the Standard Deviation (1)
g. Calculate the Interquartile Range (1.5)
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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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.
Salary in Thousands Frequency
1
2
3
4
5
6
7
90 to
440 to
790 to
1140 to
1490 to
1840 to
2190 to
under
under
under
under
under
under
under
440
790
1140
1490
1840
2190
2540
9
11
10
8
4
3
5
a. Calculate the Cumulative Frequency (0.5)
b. Calculate the Mean (0.5)
c. Calculate the Median (1)
d. Calculate the Mode (0.5)
e. Calculate the Variance (1.5)
f. Calculate the Standard Deviation (1)
g. Calculate the Interquartile Range (1.5)
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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