An appraiser is valuing an 8.2-acre vacant parcel. Three similar vacant parcels sold at $88,000, $95,000, and $102,000 per acre. The appraiser concludes to the simple mean of those unit prices, and no other adjustments are needed. What is the indicated land value?
Correct Answer
B) $779,000
Mean = ($88,000 + $95,000 + $102,000)/3 = $95,000/acre; 8.2 acres × $95,000/acre = $779,000. The indicated value is $779,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: using the lowest unit rate instead of the mean gives $721,600; using the highest unit rate instead of the mean gives $836,400; adding the three rates and skipping the division by 3 gives $285,000 × 8.2 = $2,337,000.
Why This Is the Correct Answer
Option B is correct because the mean is ($88,000 + $95,000 + $102,000) ÷ 3 = $95,000 per acre, and 8.2 acres × $95,000 = $779,000. The appraiser supports the simple mean, and no other adjustments apply. Applying the mean rate to the subject's acreage gives the land indication.
Why the Other Options Are Wrong
Option A: $721,600
Option A, $721,600, uses the lowest rate instead of the mean: $88,000 × 8.2 = $721,600. The supported mean of $95,000 × 8.2 gives $779,000.
Option C: $836,400
Option C, $836,400, uses the highest rate instead of the mean: $102,000 × 8.2 = $836,400. The supported mean of $95,000 × 8.2 gives $779,000.
Option D: $2,337,000
Option D, $2,337,000, adds the three rates but skips dividing by 3: $285,000 × 8.2 = $2,337,000. The mean is $285,000 ÷ 3 = $95,000 per acre, giving $779,000.
Divide by how many
A simple mean divides the total by the number of items; three rates means divide by three.
How to use: Use this check whenever you average a set of comparable unit prices.
Exam Tip
The correct mean must fall between the lowest and highest rate; a figure outside that range signals an averaging error.
Common Mistakes to Avoid
- -Adding the rates without dividing by the count
- -Picking the highest or lowest rate without support
Concept Deep Dive
Analysis
This question tests averaging comparable unit prices and applying the result to the subject's size. The appraiser supports the simple mean of three per-acre prices, so the rates are added and divided by three. That mean rate is then multiplied by the subject's 8.2 acres.
Background Knowledge
Price per acre is a common unit of comparison for larger vacant parcels. The simple mean is the sum of the values divided by their count. An appraiser should use a measure of central tendency only when it is supported by the comparability of the sales.
Real-World Application
An appraiser valuing an 8.2-acre rural parcel finds three similar sales at $88,000, $95,000 and $102,000 per acre. Judging them equally comparable, the appraiser uses the $95,000 mean to indicate $779,000.
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