What is the range of the following capitalization rates: 7.5%, 8.2%, 6.8%, 9.1%, and 7.9%?
Correct Answer
B) 2.3%
Range is the difference between the highest and lowest values. 9.1% - 6.8% = 2.3%.
Why This Is the Correct Answer
Option B (2.3%) is correct because range is calculated by subtracting the lowest value from the highest value in the data set. The highest capitalization rate is 9.1% and the lowest is 6.8%. Therefore, the range equals 9.1% - 6.8% = 2.3%. This calculation follows the standard statistical definition of range and provides the correct measure of spread for this data set.
Why the Other Options Are Wrong
Option A: 7.9%
Option A (7.9%) represents one of the individual capitalization rates in the data set, not the range. This appears to be a distractor answer that might confuse students who don't understand that range is a calculated difference, not a single data point.
Option C: 1.5%
Option C (1.5%) is incorrect and appears to be an arbitrary number that doesn't correspond to any meaningful calculation from the given data set. It's neither the range nor any other statistical measure that can be derived from these capitalization rates.
Option D: 9.1%
Option D (9.1%) represents the highest individual capitalization rate in the data set, not the range. This is a common distractor that tests whether students understand the difference between the maximum value and the range calculation.
High-Low Range Rule
Remember 'HI-LO = RANGE-O' - take the HIghest value, subtract the LOwest value, and you get the RANGE-O (range). Visualize a thermometer where you measure the difference between the highest and lowest temperatures.
How to use: When you see a range question, immediately identify and circle the highest and lowest numbers in the data set, then subtract: High minus Low equals Range to go!
Exam Tip
Always double-check your arithmetic when calculating range, and make sure you're subtracting the smaller number from the larger number to get a positive result.
Common Mistakes to Avoid
- -Confusing range with one of the individual data points
- -Subtracting in the wrong order (low minus high instead of high minus low)
- -Confusing range with other statistical measures like mean or median
Concept Deep Dive
Analysis
This question tests understanding of basic statistical measures used in real estate appraisal, specifically the concept of range. Range is a fundamental measure of variability that shows the spread between the highest and lowest values in a data set. In appraisal work, understanding range is crucial when analyzing comparable sales, rental rates, or capitalization rates to assess market conditions and data reliability. The range helps appraisers identify outliers and understand the consistency of market data they're working with.
Background Knowledge
Range is a basic statistical measure that quantifies the spread or variability in a data set by calculating the difference between the maximum and minimum values. In real estate appraisal, statistical analysis of market data is essential for supporting value conclusions and demonstrating the reliability of comparable sales or income data.
Real-World Application
Appraisers use range analysis when reviewing capitalization rates from comparable properties to determine if their selected cap rate falls within a reasonable market range, helping to support their income approach valuation and identify any outliers that might need further investigation.
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