The range of sale prices for comparable properties is $45,000. If the lowest sale price is $235,000, what is the highest sale price?
Correct Answer
B) $280,000
Why this is correct: The range is defined as Highest Value - Lowest Value. Therefore, Highest Value = Lowest Value + Range. Calculation: 235000 (lowest) + 45000 (range) = 280000. Why the other choices are wrong: 45000 is just the range, not the highest price. 190000 incorrectly subtracts the range. 235000 is the lowest price, not the highest. Exam tip: Range = High - Low. To find the high, add the range to the low. To find the low, subtract the range from the high.
Why This Is the Correct Answer
Option A ($280,000) correctly applies the range formula: Range = Highest Value - Lowest Value, which can be rearranged to: Highest Value = Range + Lowest Value. Substituting the given values: Highest Value = $45,000 + $235,000 = $280,000. This demonstrates proper understanding of the mathematical relationship between range, minimum, and maximum values in a dataset.
Why the Other Options Are Wrong
Option A: $45,000
Option A ($45,000) provides the range value itself rather than calculating the highest sale price, demonstrating confusion between the range measurement and the actual highest value in the dataset.
Option C: $190,000
Option C ($190,000) incorrectly subtracts the range from the lowest value ($235,000 - $45,000 = $190,000), which would actually give a value lower than the stated minimum price, making it mathematically impossible.
Option D: $235,000
Option D ($235,000) simply restates the lowest sale price without performing any calculation, failing to account for the range and suggesting no variation in the comparable sales data.
Range Bridge Formula
Remember 'Range is the BRIDGE between Low and High' - Range = High - Low, so High = Low + Range (you cross the bridge by adding the range to the low end to reach the high end)
How to use: When you see a range problem, visualize crossing a bridge from the lowest point to the highest point - the range tells you how far you need to travel (add) to get from low to high
Exam Tip
Always write out the range formula (Range = High - Low) and then algebraically solve for the unknown variable to avoid calculation errors
Common Mistakes to Avoid
- -Subtracting the range from the lowest value instead of adding it
- -Confusing the range value with the actual highest or lowest sale price
- -Forgetting to rearrange the range formula when solving for the highest value
Concept Deep Dive
Analysis
This question tests understanding of basic statistical range calculations, which are fundamental in real estate appraisal for analyzing comparable sales data. The range represents the spread between the highest and lowest values in a dataset, providing insight into market variability and helping appraisers assess the reliability of their comparable sales. Understanding range calculations is essential for statistical analysis of market data and forms the foundation for more complex appraisal adjustments and market analysis techniques.
Background Knowledge
Range is a basic measure of dispersion in statistics that shows the spread of data points by calculating the difference between the maximum and minimum values. In real estate appraisal, understanding range helps appraisers evaluate the consistency and reliability of comparable sales data.
Real-World Application
Appraisers use range analysis when reviewing comparable sales to identify outliers and assess market consistency - a large range might indicate diverse property types or market conditions requiring further investigation
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