251x0815 (Corrected) 6/6/08
ECO251 QBA1
FIRST EXAM
June 11, 2008
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. Show your work! The exam is normed on 50 points,
so that any grade above 48 is an A+ and grades wrap around.
Part I. (7 points)
The following numbers are to be considered a sample of prices of gasoline taken at five gas stations.
x1
4.14 4.19 4.25 4.01 3.99
Compute the following: Show your work!
a) The Median (1)
b) The Standard Deviation (3)
c) The 3rd quintile (2)
d) The Coefficient of variation (1)
Extra credit beyond this point!
e) The harmonic mean (1.5)
f) The root-mean square (1.5)
g) The geometric mean (3 ways!) (3)
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251x0815 (Corrected) 6/6/08
Part II. (18 points) According to Anderson, Sweeny and Williams a bank found the following as a sample
of 30 waiting times (in seconds) for service.
Row
1
2
3
4
5
Time
60-119.99
120-179.99
180-239.99
240-299.99
300-359.99
Frequency
6
10
8
4
2
a. Calculate the Cumulative Frequency (1)
b. Calculate the Mean (1)
c. Calculate the Median (2)
d. Calculate the Mode (1)
e. Calculate the Variance (3)
f. Calculate the Standard Deviation (2)
g. Calculate the Interquartile Range (3)
h. Calculate a Statistic showing Skewness and interpret it (3)
i. Make a frequency polygon of the data (Neatness Counts!)(2)
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251x0815 (Corrected) 6/6/08
(Blank page for calculations)
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251x0815 (Corrected) 6/6/08
Part III. Multiple choice (12 points). Note: If you say ‘None of the above,’ you should supply a correct
answer to get full credit.
1. If a distribution is skewed to the right, the following must be true. (Hint: making a diagram first is a good
way to prevent errors.)
a. Mean < median < mode
b. Median < mean < mode
c. Mode < median < mean
d. Mode < mean < median
e. Mean = median = mode
f. None of the above.
2. If I have a population described as grouped data and I am using definitional formulas.
f x     0
a.

b.  f x     0
c.  f x     1
d. None of the above.
3. Which of the following does not describe a population?
a. x
b. 
c. The coefficient of variation
d. 
e. Pearson’s coefficient of skewness.
f. 
g. All of the above describe a population.
4. Mark the following items N (nominal), O (ordinal), I (interval) or R (ratio) data. If the data is interval or
ratio data, would it be considered C (continuous) or D (discrete)? (4)
a) Likert Scale - The format of a typical five-level Likert item is: 1) Strongly disagree;
2) Disagree; 3) Neither agree nor disagree; 4) Agree; 5) Strongly agree ________
b) Next year’s tuition (in dollars and cents) ________
c) Place of residence __________
d) Number of credit cards that you hold _________
5. If you make a graph to represent a data set, the following should be plotted at class midpoints.
a. An ogive
b. A frequency polygon
c. A Pareto diagram
d. All of the above
e. None of the above
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251x0815 (Corrected) 6/6/08
Part IV. (13+ points)
Table 1
Given below is a stem-and-leaf display for the amount of gas purchased at a service station. Minitab gives
the following information. (SE Mean is the standard deviation divided by the square root of n .
MTB > describe c1
Descriptive Statistics: x
Variable
x
n
25
Mean SE Mean
11.372
0.232
StDev
1.158
Minimum
9.100
Q1 Median Q3 Maximum
…………… ………… ………… 13.200
9|147
10|02238
11|125566777
12|223489
13|02
1. In Table 1, what is the median purchase? (2)
2. Create a 5-number summary from Table 1. (4)
3. In Table 1, assume that you were asked to present the data in 4 classes. Using the method you learned in
class, show how you would decide what class interval to use and list the classes below with their
frequencies. (4) [10]
Class
A
B
C
D
___
___
___
___
to
to
to
to
under
under
under
under
Frequency
___
___
___
___
___
___
___
___
4. In Table 1, according to the Tchebyschev inequality, what is the minimum number of observations that
should be between 9.056 and 13.688? What would the empirical rule say? Should the empirical rule apply
here? Why? (4)
5. Which of the following are not sensitive to extreme values? (Circle all correct answers.) (3)
a. The mode
b. The mean
c. The variance
d. The coefficient of variation
e. k 3 , the third k-statistic.
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