Observed sale prices are $80,000, $90,000, $100,000, $110,000. Calculate the range (maximum−minimum), to the nearest dollar.
Correct Answer
D) $30,000
110000−80000=30000. The range is a spread measure; the average or maximum alone does not answer the question.
Why This Is the Correct Answer
Option D is correct because the maximum price is $110,000 and the minimum is $80,000. The range is $110,000 − $80,000 = $30,000. It describes the spread between the extremes.
Why the Other Options Are Wrong
Option A: $95,000
Option A, $95,000, is the mean: the prices total $380,000, and $380,000 / 4 = $95,000. The range is $110,000 − $80,000 = $30,000.
Option B: $110,000
Option B, $110,000, is the maximum price only. The range subtracts the minimum: $110,000 − $80,000 = $30,000.
Option C: $20,000
Option C, $20,000, subtracts the wrong pair of prices, such as $110,000 − $90,000 or $100,000 − $80,000, so one extreme is missed. The range uses the highest and lowest prices: $110,000 − $80,000 = $30,000.
Top minus bottom
Range means the highest value minus the lowest value, nothing more.
How to use: Use this to quickly calculate or check a range answer on the exam.
Exam Tip
Before subtracting, mark the single highest and single lowest prices; a difference between any other pair understates the range.
Common Mistakes to Avoid
- -Reporting the maximum value instead of the range
- -Using the mean as a measure of spread
- -Subtracting a non-extreme price instead of the minimum or maximum
Concept Deep Dive
Analysis
This question tests the range calculation on a small data set. You subtract the minimum from the maximum, $110,000 − $80,000 = $30,000. The distractors include the mean, the maximum alone and a difference between the wrong pair of prices.
Background Knowledge
The range equals the maximum value of a sample minus the minimum value. It is quick to compute but relies only on the two extreme observations.
Real-World Application
An appraiser working in a rural market finds four sales between $80,000 and $110,000. Reporting the $30,000 range helps the client understand the spread of the market evidence before adjustments.
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The base-period median sale price is $400,000 and the current-period median is $460,000. Compute the price relative defined as current ÷ base, as a decimal to three places.
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Sale prices are $380,000, $400,000, $420,000, $440,000, $460,000. Find the arithmetic mean of their absolute deviations from the sample mean. Report to the nearest dollar.