BUSI 121
Suggested Answers to Review and Discussion Questions: Lesson 9
1.
A percentage change is 100 times a fraction in which the numerator is the change in the value from
the base to the new value, and the denominator is the base value. It shows a change in a percentage
form, as opposed to in absolute numbers, to make it easier to compare data.
An index number is a measure of how a variable changes from one time period to a future time
period. It is 100 times a fraction where the denominator is the base value, while the numerator is the
final value. Note that the significant difference between a percentage change and an index number is
the differing numerators.
To summarize, a percentage change looks at the incremental change (the final value minus the base
value) relative to the base value, whereas the index number looks at the final value as a whole relative
to the base value.
An example: Dorian collects marbles. As of this morning, he had 200 marbles. However, an incident
during the day caused him to lose his marbles – 20 marbles, to be exact. He is left with 180 marbles.
The percentage change of his marbles would be:
100 
180  200
= -10%
200
Dorian presently has 10% fewer marbles than he had before.
The index number would be:
100 
180
= 90%
200
Dorian presently has 90% of the marbles that he had previously.
2.
This question is open-ended. Discuss with your fellow classmates on the course discussion forum.
You may wish to apply the percentage changes to a hypothetical salary of $50,000.
3.
This question is open-ended. Discuss with your fellow classmates on the course discussion forum.
4.
This question is open-ended. Discuss with your fellow classmates on the course discussion forum.
(Hint: what does "average" mean?)
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BUSI 121 – Review Answer Guide 9
Page 2 of 3
5.
(a)
One probable explanation would be that singles or couples without children seek smaller
condos (one bedroom, maybe one bedroom plus den), and families with more than one
child seek larger condos (with one bedroom per child or a similar arrangement). Therefore,
a condo consisting of two bedrooms and a den would be too big for singles/couples without
children, and would be too small for a family with more than one child (unless the children
share a room). Although the average of these two groups may be what was built, it does
not necessarily mean that a market exists for that particular condo size. This illustrates
some of the flaws of the mean. While it can be useful in many situations, it does not always
tell the whole story.
(b)
This question is open-ended. Discuss with your fellow classmates on the course discussion
forum.
6.
Since the range of Distribution 1 is greater than that of Distribution 2, Distribution 1 will have a
larger standard deviation. Since the coefficient of variation is defined as the standard deviation
divided by the mean, multiplied by 100, we need to consider what the mean would be, in addition to
the standard deviation. We cannot make conclusions about the coefficient of variation without
knowing the respective means of the two distributions.
7.
It is better to use relative frequencies over absolute when comparing two or more data sets because
percentages can be better compared across data sets that have a different number of observations.
8.
The mode is the only measure of central tendency which can be calculated for non-numerical values,
and as it would be impossible to calculate the mean or median in this case, the mode is the most
appropriate measure. The mode would give you the decorating style most frequently mentioned, but it
is possible that there may be more than one mode or none at all.
9.
The mean (μ) and the standard deviation (σ) are measured in days, while variance (σ2) will have a
unit value of days squared.
10.
The few billionaire subscribers will cause the data on Fortune readers to be skewed to the right. That
is, a few extremely high values will increase the mean value but will have no impact on the median.
Thus, it is the case that the mean value would have to be the greater of the two ($2,500,000). This
problem tests the student's knowledge of how the mean can be affected by outliers while the median
is resistant to such occurrences.
11.
Answer: 2
Option (2) is false; variables are frequently denoted by subscripts, not superscripts.
12.
Answer: 3
Option (3) is false; the mode is not always a good measure of central tendency as there may be more
than one mode and there may not be a mode The other statements are true.
13.
Answer: 2
Option (2) is false; the midpoint cannot be calculated when there is an OPEN-ENDED group because
both bounds are not known. If the bounds are known, as in a close-ended group, the midpoint can be
calculated as the arithmetic mean of the two group bounds.
© UBC Real Estate Division 2015
BUSI 121 – Review Answer Guide 9
14.
Page 3 of 3
Answer: 1
Option (1) is false; when there is a large amount of data, the lines in the graphs and charts may be
drawn as continuous curves.
15.
Answer: 4
None of the above answers are true. With a unimodal (one mode) distribution and a perfectly
symmetrical distribution, the mean, the median, and the mode must all be the same.
16.
Answer: 3
A decrease in the value of the standard deviation characterizes a data series that is less variant, or less
spread out. When the data is more tightly clustered around an arithmetic mean, the quality, or
representativeness, improves.
17.
Answer: 2
The variable with the COV closest to zero has the tightest distribution about the mean.
© UBC Real Estate Division 2015