In a data set of comparable sales, the range is $45,000 with a highest value of $385,000. What is the lowest value?
Correct Answer
A) $340,000
Range = Highest Value - Lowest Value. Therefore, Lowest Value = Highest Value - Range. $385,000 - $45,000 = $340,000.
Why This Is the Correct Answer
Option A ($340,000) is correct because it properly applies the range formula: Range = Highest Value - Lowest Value, which can be rearranged to: Lowest Value = Highest Value - Range. Substituting the given values: $385,000 - $45,000 = $340,000. This demonstrates the inverse relationship between the components of the range calculation. The mathematical operation correctly isolates the unknown variable (lowest value) using the two known variables (highest value and range).
Why the Other Options Are Wrong
Option B: $430,000
Option B ($430,000) is incorrect because it adds the range to the highest value ($385,000 + $45,000 = $430,000) instead of subtracting it. This would actually give you a value higher than the already established highest value, which is mathematically impossible in a range calculation. This represents a fundamental misunderstanding of the range formula and would indicate a data point outside the established parameters.
Option C: $192,500
Option C ($192,500) is incorrect because it appears to divide the highest value by 2 ($385,000 ÷ 2 = $192,500), which has no relationship to the range calculation. This might represent confusion with finding a midpoint or median, but it completely ignores the given range of $45,000. This approach fails to use the critical information provided in the problem.
Option D: $45,000
Option D ($45,000) is incorrect because it confuses the range value with the lowest value in the data set. While $45,000 is the range (the difference between highest and lowest values), it is not the actual lowest value itself. This represents a fundamental misunderstanding of what range measures versus what it contains.
The Range Rearrangement Rule
Remember 'HLR' - Highest minus Lowest equals Range. When you need to find the missing piece, rearrange: H - L = R becomes L = H - R or H = L + R. Think of it as a simple subtraction family: if 10 - 3 = 7, then 10 - 7 = 3.
How to use: When you see a range problem, immediately write down H - L = R, then circle what you're looking for and rearrange the formula. If looking for L (lowest), cover it up and see L = H - R. Always double-check that your answer makes logical sense within the range.
Exam Tip
Always verify your range calculation makes sense: the lowest value plus the range should equal the highest value, and the lowest value should always be less than the highest value.
Common Mistakes to Avoid
- -Adding range to highest value instead of subtracting from it
- -Confusing range with the actual lowest or highest value
- -Using median or midpoint calculations instead of range formulas
Concept Deep Dive
Analysis
This question tests understanding of basic statistical measures used in real estate appraisal, specifically the concept of range in a data set. Range is a fundamental measure of dispersion that shows the spread between the highest and lowest values in a comparable sales analysis. Appraisers must be able to quickly calculate and interpret range to assess the reliability and consistency of their comparable sales data. Understanding range helps appraisers identify outliers and determine the quality of their data set for making accurate property valuations.
Background Knowledge
Range is a basic statistical measure that represents the difference between the highest and lowest values in a data set, calculated as Range = Highest Value - Lowest Value. In real estate appraisal, range helps appraisers assess the consistency and reliability of comparable sales data. A smaller range generally indicates more consistent and reliable comparables, while a larger range may suggest the need for additional adjustments or the presence of outliers.
Real-World Application
When analyzing comparable sales for a $350,000 home, an appraiser finds comps ranging from $320,000 to $380,000 (range = $60,000). This range helps determine if the comps are sufficiently similar or if adjustments are needed for a reliable valuation.
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