Observed sale prices are $180,000, $185,000, $190,000, $195,000, $200,000. Calculate the range (maximum−minimum), to the nearest dollar.
Correct Answer
A) $20,000
200000−180000=20000. The range is a spread measure; the average or maximum alone does not answer the question.
Why This Is the Correct Answer
Option A is correct because the maximum price is $200,000 and the minimum is $180,000, so the range is $200,000 − $180,000 = $20,000. The range describes the full spread of the observations.
Why the Other Options Are Wrong
Option B: $190,000
Option B, $190,000, is the mean (and median) of the five prices, a measure of center. The range is $200,000 − $180,000 = $20,000.
Option C: $200,000
Option C, $200,000, is only the maximum observation. The range subtracts the minimum: $200,000 − $180,000 = $20,000.
Option D: $15,000
Option D, $15,000, subtracts the wrong pair of prices, such as $200,000 − $185,000 or $195,000 − $180,000, so one of the extremes is missed. The range uses the highest and lowest values: $200,000 − $180,000 = $20,000.
High minus low
The range is the highest value minus the lowest value, nothing more.
How to use: Use this to compute the range quickly from any list of prices.
Exam Tip
Distractors often include the average, the maximum or a difference between two non-extreme values; the range uses only the highest and lowest prices.
Common Mistakes to Avoid
- -Reporting the mean as the range
- -Giving only the maximum value
- -Subtracting the wrong pair of values
Concept Deep Dive
Analysis
This question tests the range as a measure of spread. The range is the maximum minus the minimum, so both extreme values must be identified first. For these prices, $200,000 − $180,000 = $20,000.
Background Knowledge
The range is the maximum value of a sample minus the minimum value. It is simple but sensitive to a single extreme observation. Appraisers often report it with the median or mean to describe a market.
Real-World Application
An appraiser notes that five comparable sales ranged from $180,000 to $200,000. Reporting the $20,000 range helps the reader see how widely the sale prices are spread.
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