The following data set represents recent sale prices: $180,000, $185,000, $190,000, $195,000, $200,000. What is the range?
Correct Answer
A) $20,000
Why this is correct: The range is a measure of dispersion, calculated as the highest value minus the lowest value. For the data set ($180,000, $185,000, $190,000, $195,000, $200,000), the highest is $200,000 and the lowest is $180,000. Therefore, the range is $200,000 - $180,000 = $20,000. Why the other choices are wrong: The choice "$950,000" is the sum of all sale prices, not the range. The choice "$190,000" is the median or mean, not the range. The choice "$10,000" is an incorrect calculation, possibly from subtracting non-extreme values. Exam tip: For range, always identify the single highest and single lowest numbers in the list before subtracting.
Why This Is the Correct Answer
Option A ($20,000) is correct because range is calculated by subtracting the lowest value from the highest value in the dataset. The highest sale price is $200,000 and the lowest is $180,000. Therefore, $200,000 - $180,000 = $20,000. This represents the total spread of the sale prices in this particular market sample.
Why the Other Options Are Wrong
Option B: $950,000
Option B ($950,000) is the sum of all values in the dataset, which represents the total rather than the range. This indicates confusion between different statistical calculations.
Option C: $190,000
Option C ($190,000) represents the median (middle value) of the dataset, not the range. This is a common confusion between measures of central tendency and measures of dispersion.
Option D: $10,000
Option D ($10,000) appears to be half the correct range or possibly the difference between consecutive values in this evenly spaced dataset. This suggests confusion about the range calculation formula.
High-Low Range Rule
Remember 'Range = High minus Low' or use the acronym 'HML' (High Minus Low). Visualize a mountain range where you measure from the highest peak to the lowest valley.
How to use: When you see a range question, immediately identify the highest and lowest values in the dataset, then subtract low from high. Don't get distracted by other statistical measures.
Exam Tip
Always double-check that you're subtracting the minimum from the maximum, not the other way around, and ensure you've correctly identified the highest and lowest values in the dataset.
Common Mistakes to Avoid
- -Confusing range with median or mean
- -Subtracting maximum from minimum instead of minimum from maximum
- -Adding all values instead of finding the difference between extremes
Concept Deep Dive
Analysis
Range is a fundamental statistical measure of dispersion that quantifies the spread of data by calculating the difference between the maximum and minimum values in a dataset. In real estate appraisal, range helps appraisers understand the variability in comparable sales prices and assess market consistency. A smaller range indicates more uniform pricing, while a larger range suggests greater market volatility or diverse property characteristics. Understanding range is essential for appraisers to evaluate the reliability of their comparable sales and make appropriate adjustments.
Background Knowledge
Range is one of the simplest measures of variability in statistics, calculated as the difference between the maximum and minimum values in a dataset. In real estate appraisal, understanding data dispersion helps appraisers evaluate the consistency and reliability of comparable sales data.
Real-World Application
When analyzing comparable sales for a residential appraisal, an appraiser might find sale prices ranging from $180,000 to $200,000, giving a range of $20,000. This relatively small range suggests a stable market with consistent pricing, making the comparables more reliable for valuation purposes.
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