A dataset of comparable sales shows the following values: $310,000, $315,000, $320,000, $325,000, $390,000. What is the range of this dataset?
Correct Answer
D) $80,000
Why this is correct: The range is a measure of dispersion calculated as the difference between the maximum and minimum values in a dataset. Here, the highest value is $390,000 and the lowest is $310,000. The calculation is: $390,000 - $310,000 = $80,000. Why the other choices are wrong: '$15,000' might be the difference between some consecutive values but not the overall range. '$332,000' is close to the mean, not the range. '$324,000' is close to the median, not the range. Exam tip: Range = Highest Value - Lowest Value. It's sensitive to outliers, like the $390,000 sale in this set.
Why This Is the Correct Answer
Option A ($80,000) is correct because range is calculated as the difference between the maximum and minimum values in the dataset. The highest value is $390,000 and the lowest value is $310,000. Subtracting the minimum from the maximum: $390,000 - $310,000 = $80,000. This represents the total spread of the comparable sales data.
Why the Other Options Are Wrong
Option A: $15,000
Option A ($15,000) represents the difference between consecutive values in the lower portion of the dataset (e.g., $325,000 - $310,000 = $15,000), but this is not the range. This shows a misunderstanding of range as the difference between adjacent values rather than the total spread.
Option B: $332,000
Option B ($332,000) appears to be an attempt to calculate some form of average or sum, but it's not the range. This value doesn't correspond to any standard statistical measure for this dataset and shows a misunderstanding of what range represents.
Option C: $324,000
Option C ($324,000) is close to the mean (average) of the dataset, which would be $332,000, but it's neither the mean nor the range. This suggests confusion between different statistical measures used in comparable sales analysis.
Range = Reach from Bottom to Top
Remember 'Range = Reach' - imagine reaching from the lowest point to the highest point. Just like measuring how far you can reach with your arms stretched out, range measures how far the data stretches from bottom (minimum) to top (maximum).
How to use: When you see a range question, immediately identify the highest and lowest numbers in the dataset, then subtract: Highest - Lowest = Range. Think 'reach from bottom to top' to remember the subtraction direction.
Exam Tip
Always organize the data in ascending order first to easily identify the minimum and maximum values, then perform the simple subtraction to avoid calculation errors.
Common Mistakes to Avoid
- -Calculating the mean instead of the range
- -Subtracting consecutive values rather than max minus min
- -Adding values instead of subtracting them
Concept Deep Dive
Analysis
This question tests understanding of basic statistical measures used in real estate appraisal, specifically the range calculation. Range is a fundamental measure of data dispersion that shows how spread out comparable sales values are, which is crucial for determining the reliability and consistency of market data. In appraisal practice, understanding the range helps appraisers assess whether their comparable sales are tightly clustered (indicating a stable market) or widely dispersed (suggesting market volatility or the need for adjustments). The calculation is straightforward but essential for statistical analysis of comparable sales data.
Background Knowledge
Range is the simplest measure of variability in statistics, calculated as the difference between the highest and lowest values in a dataset. In real estate appraisal, statistical measures like range, mean, and median are essential tools for analyzing comparable sales data and determining market trends and property values.
Real-World Application
Appraisers use range to assess market stability - a small range indicates consistent pricing in a neighborhood, while a large range might suggest diverse property types, market volatility, or the need to refine comparable selection criteria.
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