After independently assessing comparability, an appraiser retains three adjusted sale indications: $305,000, $309,000 and $312,000. For a numerical summary only, what is their arithmetic mean, rounded to the nearest dollar?
Correct Answer
A) $308,667
The three retained indications sum to $926,000. Dividing by 3 gives $308,666.67, or $308,667 to the nearest dollar. No universal gross-adjustment percentage cutoff is implied, and this descriptive mean is not a substitute for a supported reconciliation.
Why This Is the Correct Answer
Option A is correct because $305,000 + $309,000 + $312,000 = $926,000, and $926,000 / 3 = $308,666.67. Rounded to the nearest dollar, the arithmetic mean is $308,667. This figure is a descriptive summary only; the reconciled indication still depends on the comparability of each sale.
Why the Other Options Are Wrong
Option B: $309,000
Option B, $309,000, is the median, the middle of the three figures when ranked, not the mean. The mean is $926,000 / 3 = $308,667.
Option C: $305,000
Option C, $305,000, is the lowest of the three indications, not their mean. The mean is ($305,000 + $309,000 + $312,000) / 3 = $308,667.
Option D: $312,000
Option D, $312,000, is the highest of the three indications, not their mean. The mean is $926,000 / 3 = $308,667.
Mean adds, median ranks
The mean adds all the figures and divides by the count; the median just ranks them and takes the middle.
How to use: Use this to avoid picking the median when a question asks for the mean.
Exam Tip
Check whether the question asks for the mean, the median or a range endpoint, since all three often appear among the options.
Common Mistakes to Avoid
- -Choosing the middle figure (the median) when the mean is asked for
- -Rounding $308,666.67 down to $308,666
- -Treating the mean as the reconciled value without analysis
Concept Deep Dive
Analysis
This is an arithmetic question on the mean of three adjusted sale indications. Add the three figures and divide by three, then round to the nearest dollar. The question also reminds you that the mean is only a numerical summary, not a substitute for a reasoned reconciliation.
Background Knowledge
The arithmetic mean is the sum of the values divided by the number of values, while the median is the middle value and the range runs from the lowest to the highest. These statistics describe the spread of indications. In reconciliation, the appraiser still weighs each sale's comparability and reliability rather than adopting a statistic mechanically.
Real-World Application
An appraiser notes in her workfile that her three adjusted sales average $308,667 and have a median of $309,000. She uses those figures to describe how tightly the sales cluster. Her reported indication is based on which sales are most comparable, and she explains that choice.
More Reconciliation Questions
In a cost approach for an improved property, an appraiser estimates site value by sales comparison, allocation and extraction, then settles on one site-value figure before final reconciliation. How is this step best described?
An extraordinary assumption was reasonably supported, properly used and disclosed in an appraisal report. Later, the assumed information is found to be false. Which conclusion is best supported?
An otherwise applicable valuation approach cannot be developed reliably from the available data. The remaining scope can produce credible assignment results. What should the appraiser do?
May an appraiser use a hypothetical condition in any assignment?
An appraisal has a current effective date and permits an extraordinary assumption if its requirements are met. Which situation involves uncertain information rather than a fact known to be contrary to reality on that date?
Why must a report identify any real property interest that is being excluded from the value opinion?
Which review best helps explain divergent cost, sales-comparison and income indications?
Two value indications are $340,000 and $392,000. What is the difference as a percentage of the lower indication, rounded to one decimal place?
An unauthorized third party requests a lender-client’s report. No due-process or other permitted disclosure exception applies. How should the appraiser respond?
An appraiser proposes to assume there are no hidden defects. Which fact would characterize that assumption as extraordinary under the USPAP 2024 definition, rather than justify dismissing it as routine boilerplate?
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During reconciliation, a pending rezoning is known to buyers but is reflected in only one of the three indications. What should the appraiser do?
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