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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)
Use the eleven numbers that you used in the second problem in the take-home exam. (If you don’t have
them – take your student number plus the numbers (3, 6, 9, 9, 21) . Example: Seymour Butz’s student
number is 876509, so he gets 8, 7, 6, 5, 0, 9, 3, 6, 9, 9, 21. Of course, he has read “Things That You Should
Never Do on an Exam or Anywhere Else” and knows that he can’t use them this way. )
Compute the following:
a) The Median (1)
b) The Standard Deviation (3)
c) The 2nd Quintile (2)
d) The Coefficient of variation (1)
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Part II.
1. The problem in the textbook that gives the data used in the take home also gives the braking
distance for a sample of domestic made cars. It is presented below.
Distance(feet) frequency
210
220
230
240
250
260
270
280
290
300
310
–
–
–
–
-
220
230
240
250
260
270
280
290
300
310
320
1
1
1
1
4
3
6
4
2
2
0
Minitab was used to calculate statistics from these data. It claims the following: x  269 , s 2  525 ,
k 3  7281 .61. You will not be able to use any of these numbers in b) or c) without some
manipulation in parts b and c. Answers below are not acceptable unless you give some evidence in the
sample statistics.
a) Do American cars have a shorter braking distance? Compare all 3 measures of central
tendency. (2)
b) Are American cars more consistent in braking distance than foreign cars? Use a
dimension-free measurement of variability. (2)
c) Compare the direction and degree of skewness in the two distributions. Use one
dimension- free measure of skewness. (2)
d) Write a 5-number summary of the results from the first take-home problem. (2) 15
2.
The following numbers refer to miles-per-gallon of a sample of vehicles (Bowerman and
O’Connell). This has been corrected.
Class (mpg)
F
f rel
f
Frel
29.8 - 30.3
____
____
____
.0612
30.4 – 30.9
____
____
____
.2449
31.0 – 31.5
____
____
24
____
31.6 – 32.1
____
.2653
35
.7551
32.2 – 32.7
9
.1837
46
.9388
32.8 – 33.3
3
.0612
49
1.000
Fill in the missing numbers. (5)
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Part III. (At least 22 points – 2 points each unless marked)
1.
Mark the variables below as qualitative (A) or quantitative (B)
a) Number of days a patient stays at a spa
b) Preferences for 10 beers on a 1st to 10th scale
c) Method of contraception
d) Per cent change in population between censuses
2.
Which of the following is an example of continuous ratio data?
a) Number of days a patient stays at a spa
b) Preferences for beers on a 1 to 10 scale
c) Method of contraception
d) Per cent change in population between censuses
e) None of the above.
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3.
A summary measure that is computed to describe a characteristic of a population is called
a) a parameter.
b) a census.
c) a statistic.
d) An inference
e) None of the above
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4.
In general what are the two types of descriptive statistic most frequently reported
a) Measures of kurtosis and measures of dispersion
b) Measures of kurtosis and measures of skewness
c) Measures of kurtosis and measures of central tendency
d) Measures of dispersion and measures of skewness
e) Measures of dispersion and measures of central tendency
f) Measures of skewness and measures of central tendency
g) None of the above.
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Mark the following formulas (1 each) . Circle a, b or c. b) must be filled in if you
have circled it.
5.
Coefficient of Excess
2 
4
3
4
or g 2 
k4
s4
a) This cannot be negative.
b) If this is negative it means the distribution is ______
c) This can be negative, but it has no special meaning.
6.
7.
8.



n
x 3  3x
x 2  2nx 3
(n  1)( n  2)
a) This cannot be negative.
b) If this is negative it means the distribution is ______
c) This can be negative, but it has no special meaning.
k 3
x
x
n
a) This cannot be negative.
b) If this is negative it means the distribution is ______
c) This can be negative, but it has no special meaning.
s2 
x
2
 nx 2
n 1
a) This cannot be negative.
b) If this is negative it means the distribution is ______
c) This can be negative, but it has no special meaning.
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Exhibit 1: The following is taken from Problem 3.22 in the text. The data below represent sales tax
receipts submitted to a township government by 50 businesses in one quarter.
Sales Taxes ($000)
10.3
13.0
11.1
10.0
9.3
11.1
11.2
10.2
12.9
11.5
9.6 9.0 14.5 13.0 6.7 11.0 8.4 10.3
7.3 5.3 12.5 8.0 11.8 8.7 10.6 9.5
11.1 9.9 9.8 11.6 15.1 12.5 6.5 7.5
9.2 10.0 12.8 12.5 9.3 10.4 12.7 10.5
10.7 11.6 7.8 10.5 7.6 10.1 8.9 8.6
The text solution manual offers the following results.
(a) Stem-and-leaf display of Quarterly Sales Tax Receipts
5
6
7
8
9
10
11
12
13
14
15
3
57
3568
04679
02335689
00123345567
011125668
555789
00
5
1
(b)  = 10.28
(c)
(d)
(e)
(f)
9.
 2 = 4.1820,  = 2.045
64% of the receipts are within 1 standard deviations of the mean.
94% of the receipts are within 2 standard deviations of the mean.
100% of the receipts are within 3 standard deviations of the mean.
According to the stem and leaf display, what percent of the receipts were below $7000? (1)
10. If the researcher was directed to present the data in 6 classes, what should the class interval
be? Show your calculations.
15
11. Show the actual intervals you might use.
Class
A
B
C
D
E
F
From
17
to
12. The description above says that 64% of the receipts are within 1 standard deviations of the
mean. Between what numbers does this mean? How does this compare with the empirical
rule? Why might there be a discrepancy? (3)
13. The description above says that 100% of the receipts are within 3 standard deviations of the
mean. Between what numbers does this mean? How does this compare with the Chebyshev
rule? Why might there be a discrepancy? (3)
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Blank page for calculations.
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ECO251 QBA1
FIRST EXAM
October 6, 2004
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 (11 Points) Show your work!
1. The frequency distribution below represents the braking distance for a sample of foreign made cars..
Personalize the data as follows. Write down your student number. Take the last two digits of the number.
Add the largest of the two last numbers to the frequency for 300-310 and the second largest to the frequency
for 310-320. Use the results as your frequencies. For example, Seymour Butz’s student number is 876509
so he adds 0 to the last frequency and 9 to the second to last frequency and uses (1, 3, 12, 15, 22, 7, 7, 5, 2,
10, 1).
Distance (feet) frequency
210
220
230
240
250
260
270
280
290
300
310
–
–
–
–
-
220
230
240
250
260
270
280
290
300
310
320
1
3
12
15
22
7
7
5
2
1
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 showing relative or
percentage cumulative frequency (Neatness
Counts!)(1)
j. Extra credit: Put a (horizontal) box plot below
the ogive using the same scale. (1)
2. Use the frequencies you used in problem 1 in this problem as values of x .
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 ). While you’re at it, compute the sample mean and
bring it and the numbers that you used on this take-home exam to the in-class exam
(no credit until you get to the exam – but it won’t hurt).
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