After reviewing the evidence, an appraiser excludes a $509,000 indication as unrepresentative and retains $412,000, $418,000 and $421,000. What is the arithmetic mean of the three retained indications?
Correct Answer
D) $417,000
The retained values sum to $1,251,000. Divide by 3 to obtain $417,000. Including the excluded observation would calculate a different mean. This exercise stipulates the completed selection decision and does not create an automatic exclusion rule for every non-arm’s-length transaction or a universal averaging rule for final value.
Why This Is the Correct Answer
Option D is correct because 412,000 + 418,000 + 421,000 = $1,251,000, and 1,251,000 / 3 = $417,000. The excluded $509,000 indication is not part of the retained set. This exercise stipulates the selection decision and does not create a universal averaging rule for final value.
Why the Other Options Are Wrong
Option A: $440,000
Option A's $440,000 includes the excluded indication: (412,000 + 418,000 + 421,000 + 509,000) / 4 = 1,760,000 / 4 = $440,000. The question asks for the mean of the three retained values, which is $417,000.
Option B: $421,000
Option B's $421,000 is simply the highest retained indication, not a mean. Averaging the three retained values gives 1,251,000 / 3 = $417,000.
Option C: $418,000
Option C's $418,000 is the median, the middle retained value, not the arithmetic mean. The mean is 1,251,000 / 3 = $417,000.
Mean means sum and divide
Add only the values you kept, then divide by how many you kept.
How to use: Use this when a question asks for a mean after excluding data.
Exam Tip
Check whether excluded figures belong in the calculation, and do not confuse the mean with the median or the highest value.
Common Mistakes to Avoid
- -Including the excluded indication in the mean
- -Confusing the median with the mean
- -Treating the mean as the automatic final value
Concept Deep Dive
Analysis
This question tests computing an arithmetic mean of only the retained indications. The $509,000 figure has already been excluded, so it must stay out of the calculation. Add the three retained values and divide by three.
Background Knowledge
The arithmetic mean is the sum of values divided by their count, while the median is the middle value of an ordered set. Excluding an unrepresentative observation changes the mean. In appraisal, statistical summaries can assist analysis but do not replace judgment about which approach best measures the property's benefits.
Real-World Application
An appraiser reviewing four sales excludes one that verification shows was a non-market transaction. The remaining three sales are analyzed further. The appraiser notes their mean and median as context while weighting them by comparability.
More Reconciliation Questions
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