Capitalization rates are 7.5%, 8.2%, 6.8%, 9.1%, 7.9%. What is their range in percentage points, to one decimal place?
Correct Answer
C) 2.3 percentage points
9.1−6.8=2.3 percentage points. This is a difference between percentage rates, not a relative percentage change.
Why This Is the Correct Answer
Option C is correct because the highest rate is 9.1% and the lowest is 6.8%, so the range is 9.1 − 6.8 = 2.3 percentage points. This is a simple difference between two rates, not a relative percentage change.
Why the Other Options Are Wrong
Option A: 9.1 percentage points
Option A, 9.1 percentage points, is just the highest rate in the set. The range subtracts the lowest rate from it: 9.1 − 6.8 = 2.3 percentage points.
Option B: 7.9 percentage points
Option B, 7.9 percentage points, is the median of the ordered rates (6.8, 7.5, 7.9, 8.2, 9.1), not the range. The range is 9.1 − 6.8 = 2.3 percentage points.
Option D: 6.8 percentage points
Option D, 6.8 percentage points, is just the lowest rate in the set. The range is the highest minus the lowest: 9.1 − 6.8 = 2.3 percentage points.
Top minus bottom
Range is the distance from the top of the list to the bottom: highest minus lowest.
How to use: Use this to compute the range of any set of values, including cap rates.
Exam Tip
Sort the values first so you can quickly spot the highest and lowest. Answer choices that equal a single data value are usually not the range.
Common Mistakes to Avoid
- -Reporting the highest or lowest value instead of the difference
- -Confusing the range with the median
- -Describing a difference between rates as a percent change rather than percentage points
Concept Deep Dive
Analysis
This question tests the range of a set of capitalization rates. The range is the largest value minus the smallest value. Because the inputs are percentages, the difference is expressed in percentage points.
Background Knowledge
The range is the maximum value of a sample minus the minimum value, and it is the simplest measure of dispersion. Because it depends only on the two extremes, it is sensitive to outliers. When the data are rates, a difference between two rates is reported in percentage points.
Real-World Application
An appraiser extracts overall capitalization rates from five comparable apartment sales. Reporting a range of 2.3 percentage points shows how widely the market-derived rates are spread before the appraiser reconciles a rate for the subject.
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