Download Numerical Descriptive Measures

BRIEF SOLUTIONS
Numerical Descriptive
Measures
WEEK TWO
This worksheet relates to chapter three of the text
book (Statistics for Managers 4th Edition).
Past exam questions are very important to give you
an idea of what to expect in an exam and how
prepared you are. You may need to practice doing
questions quickly so that when you are in the exam
you don’t panic.
CALCULATION QUESTIONS
1. Using the following data to calculate the mean, median, mode, 1st quartile
and 3rd quartile. Are there any outliers?
5
7
8
9
9
9
9
10
Mean:
11.63
Median:
position = 6
value = 9
Mode:
9
1st quartile:
position = 3
value = 8
3rd quartile:
position = 9
value = 10
Outliers:
40
9
10
12
40
2.
The price of renting a car for a week, with manual transmission but
declining collision damage waiver in 12 European countries is presented
in the table. Calculate the mean and interquartile range.
Country
Austria
Belgium
Britain
Denmark
France
Ireland
Netherlands
Norway
Spain
Sweden
Switzerland
Germany
Rental Price
239
179
229
181
237
216
194
241
154
280
254
192
In order:
154 179 181 192 194 216 229 237 239 241 254 280
Mean: 216.33
IQ range:
Q1 position: 3.25
Q1 value: 181 (ie. 3rd score)
Q3 position: 9.75
Q3 value: 241 (ie. 10th score)
∴ IQ range
=
=
241 – 181
60
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Mid Semester, April 2005
At the end of each chapter of the textbook
there is a summary flow chart. They can be
really useful to work out exactly how all of
the concepts fit together.
3.
Calculate the coefficient of variation for the following two sets of data
using the given information. Which has greater variation? Why do we
use the coefficient of variation here, and not the standard deviation or
variance?
Grams of cereal
400
392
415
387
407
Kilograms of rock
4000
4365
3625
4184
3748
Cereal
Rock
Mean = 400.2
SD = 11.256
CV = 2.81%
Mean = 3984.4
SD = 304.135
CV = 7.633%
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MULTIPLE CHOICE PRACTICE
1.
An error has been made in the scaling of exam marks, and five extra
marks are given to every student. The result is that:
(a) The mean score increases by 5 but the standard deviation does
not change
(b) Both the mean and the standard deviation increase by 5
(c) The mean increases by 5 and the standard deviation increases by
sqrt5
Final Exam, June 2003
(d) The mean and variance increase by 5
Final Exam, June 1997
2.
The correlation coefficient between the price of broccoli and the amount
of rain that fell during the growing season is calculated to be -0.878. This
indicates that
(a)
(b)
(c)
(d)
3.
a large amount of rain causes high prices
prices tend to be low when rainfall is high
prices tend to high when rainfall is high
a lack of rain causes prices to rise
A student scored 70% on the mid-semester exam, 83% on the CML’s
and 76% on the final exam. Find the average score if the mid-semester
exam was worth 25% and the final exam was worth 55%.
(a) 76.3%
(b)75.9%
(c) 78.35%
(d) 71.75%
4.
Final Exam, June 2004
Mid Semester, April 2000;
Mid Semester, May 2003
The geometric mean
(a)
is a better measure of dispersion than the arithmetic mean
(b) is preferable to an arithmetic mean when the data fluctuates
between positive to negative
(c) indicates the multiplicative effects over time in compound
interest situations
Mid Semester, April 2005
(d) both (b) and (c) are true
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5.
The following is the descriptive statistics printout for a set of data, from
Excel.
Mean
Median
Mode
Standard Deviation
Minimum
Maximum
Sum
Count
473.4615
451
n/a
210.7663
264
1049
6155
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Which of the following is true?
(a)
(b)
(c)
(d)
the distribution is right-skewed
the best measure of central tendency is the median
both (a) and (b) are correct
none of the above are correct
Mid Semester, April 2005
13
notes
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