251x0611 2/10/06
ECO251 QBA1
FIRST EXAM
February 16 and 17, 2006
ECO251 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)
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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.
(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 is
a) 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 is
a) 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 is
a) Deductive reasoning
b) Inductive reasoning
c) Census taking
d) Sampling
e) None of the above.
[11]
6.
Observations about a discrete quantitative variable
a) Can be made in only two categories
b) 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) GPA
b) Number of credits earned
c) Major area of study
d) Grade obtained in a statistics course.
[17]
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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 skewness
b) The coefficient of variation.
c) The mean
d) All of the above will change
e) None of the above will change
.
[19]
TABLE 2-13
Given 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 | 147
10 | 02238
11 | 135566777
12 | 223489
13 | 02
9.
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]
A
B
C
D
E
F
__
__
__
__
__
__
Class
to under
to under
to under
to under
to under
to under
__
__
__
__
__
__
Frequency
__
__
__
__
__
__
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]
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13. What characteristic do the mean, median and mode have that they do not share with the
variance and the interquartile range? (1)
[33]
14. 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
Total
North America
54.8
5.3
Central and South America
Western Europe
Africa
Middle East
Far East and Oceania
Eastern Europe and CIS
95.2
17.2
74.9
683.6
44.0
59.0
9.2
1.7
7.3
66.5
4.3
5.7
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Blank page for calculations.
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ECO251 QBA1
FIRST EXAM
February 16 and 17, 2006
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. 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
-.95
-.75
-.55
-.35
-.15
.05
.25
.45
.65
to
to
to
to
to
to
to
to
to
Frequency
-.76
-.56
-.36
-.16
.04
.24
.44
.64
.84
1
2
9
25
65
35
10
5
1
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 an ogive of the data (Neatness
Counts!)(1)
j. Extra credit: Put a (horizontal) box plot below
the ogive chart using the same horizontal scale
(1)
2. The following problems (1 point each) are given in their raw form. Personalize them by using the third
to last and second to last numbers in your student number. Add them as percents to the first two percents in
a) and then add them to the first two numbers in b) and finally in c) divide them by 100 and add them to the
first two numbers. For example, Seymour Butz’s student number is 876509, so he uses 5 and 0. This means
in a) the percents are 5% + 5% =10%, 10% + 0% = 10%, -1%, 3%, and 6%, in b) the speeds are 55 + 10 =
65, 30 + 0 = 30, 70, 35 and 80 and in c) the numbers are 0.01 + 0.05 = 0.06, 0.25 + 0.00 = 0.25, 0.37, 0.26,
0.85 and 0.27
a) Geometric Mean
Over 5 years GDP grew at 5%, 10%, -1%, 3% and 6%. Modify these as was done in the example given in
class and use the geometric mean to find the average rate of growth.
b) Harmonic mean
I drive 300 miles a day, on the first day at (an average of) 55 mph, on the second at 30 mph, on the third at
70 mph, on the 4th at 35 mph and on the last at 80 mph. Use the harmonic mean to find my average speed
over the 5 days.
c) Root-mean-square
Find the rms of the following numbers: 0.01, 0.25, 0.37, 0.26, 0.85 and 0.27.
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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