Three competitive vacant land sales closed at $210,000, $225,000, and $240,000 after cash-equivalent adjustment. What land value does the mean of these sales indicate?
Correct Answer
B) $225,000
Add the three stated indications, $210,000 + $225,000 + $240,000 = $675,000, then divide by three: $225,000. This is the requested arithmetic mean; an actual reconciliation must also consider comparability and reliability, rather than automatically averaging every sale.
Why This Is the Correct Answer
Option B is correct because the three adjusted prices total $210,000 + $225,000 + $240,000 = $675,000. Dividing by three gives a mean of $225,000.
Why the Other Options Are Wrong
Option A: $210,000
Option A, $210,000, is the lowest of the three sales, not their mean. The mean is $675,000 ÷ 3 = $225,000.
Option C: $337,500
Option C, $337,500, divides the $675,000 total by 2 instead of 3. There are three sales, so the mean is $675,000 ÷ 3 = $225,000.
Option D: $675,000
Option D, $675,000, is the sum of the three sales ($210,000 + $225,000 + $240,000) with the step of dividing by three left out. The mean is $675,000 ÷ 3 = $225,000.
Sum, then divide by count
The mean is the total of all values divided by how many there are. Three sales means divide the total by three.
How to use: Use this two-step routine for any mean of adjusted sale prices.
Exam Tip
Answer choices often include the lowest sale, a wrong divisor and the undivided total. Add the sales, then divide by how many there are.
Common Mistakes to Avoid
- -Choosing the lowest sale or dividing by the wrong count
- -Forgetting to divide the total by the number of sales
- -Treating the mean as the final value without reconciliation
Concept Deep Dive
Analysis
This question tests computing an arithmetic mean of adjusted land sale prices. You add the three cash-equivalent prices and divide the total by three. In practice, reconciliation also weighs comparability, but the question asks only for the mean.
Background Knowledge
The arithmetic mean is the sum of values divided by their count. Appraisers may calculate a mean of adjusted sales, but final reconciliation should consider the reliability and comparability of each sale rather than averaging mechanically.
Real-World Application
An appraiser has three competitive vacant lot sales adjusted to cash equivalency. She computes their mean as a check, then reviews which sale is most comparable before reconciling a land value.
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