The sale prices in a neighborhood are: $180,000, $195,000, $185,000, $200,000, $190,000. What is the range of these prices?
Correct Answer
B) $20,000
Why this is correct: Range = Highest Value - Lowest Value. Here, highest is $200,000, lowest is $180,000. $200,000 - $180,000 = $20,000. Why the other choices are wrong: "$200,000" is the highest price, not the range. "$950,000" is the sum of all prices. "$190,000" is close to the mean but not the range. Exam tip: Range is a simple measure of spread. Always subtract the smallest from the largest; don't confuse it with the average.
Why This Is the Correct Answer
Option B ($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, so the range equals $200,000 - $180,000 = $20,000. This $20,000 range indicates the total spread between the most expensive and least expensive properties in this neighborhood sample.
Why the Other Options Are Wrong
Option A: $200,000
Option A ($200,000) is simply the highest value in the dataset, also known as the maximum value. While this is used in calculating the range, it is not the range itself.
Option C: $950,000
Option C ($950,000) appears to be the sum of all the sale prices ($180,000 + $195,000 + $185,000 + $200,000 + $190,000 = $950,000), which would be used to calculate the mean, not the range.
Option D: $190,000
Option D ($190,000) represents the median value of the dataset when arranged in order, not the range. The median is the middle value that separates the higher half from the lower half of the data.
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 and circle the highest and lowest values in the dataset, then subtract: Highest - Lowest = Range. Always double-check by ensuring your answer is smaller than any individual value in the dataset.
Exam Tip
Always arrange the data in ascending or descending order first to easily identify the highest and lowest values, reducing the chance of calculation errors.
Common Mistakes to Avoid
- -Confusing range with median or mean values
- -Adding all values together instead of finding the difference between extremes
- -Using the highest value alone instead of calculating the difference
Concept Deep Dive
Analysis
Range is a fundamental statistical measure that quantifies the spread or dispersion of data values in a dataset. In real estate appraisal, understanding range helps appraisers assess market variability and identify potential outliers in comparable sales data. The range provides a quick snapshot of how much variation exists in property values within a given area or market segment. While range is useful for initial data analysis, it can be heavily influenced by extreme values and should be considered alongside other statistical measures like standard deviation for comprehensive market analysis.
Background Knowledge
Range is one of the basic measures of variability in statistics, calculated as the difference between the maximum and minimum values in a dataset. In real estate appraisal, statistical measures like range help appraisers understand market conditions, identify comparable properties, and support valuation conclusions with quantitative analysis.
Real-World Application
Appraisers use range analysis when reviewing comparable sales to understand market variability. A narrow range might indicate a stable, homogeneous market, while a wide range could suggest diverse property types, market volatility, or the presence of outliers that need further investigation.
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