The subject site contains 7,500 square feet. Three cash-equivalent sales of similar vacant sites indicate $45, $48, and $51 per square foot. Based on the mean price per square foot, what is the indicated land value?
Correct Answer
B) $360,000
Mean = ($45 + $48 + $51)/3 = $48/SF; subject = 7,500 SF × $48/SF = $360,000. The indicated value is $360,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: dividing the sum of the rates by 4 instead of 3 gives $36 × 7,500 = $270,000; using the highest unit rate instead of the mean gives $382,500; adding the rates and skipping the division by 3 gives $144 × 7,500 = $1,080,000.
Why This Is the Correct Answer
Option B is correct because the mean is ($45 + $48 + $51) / 3 = $48 per SF. Multiplying by the subject's area gives 7,500 × $48 = $360,000. The question specifically asks for the mean-$/SF indication.
Why the Other Options Are Wrong
Option A: $270,000
Option A, $270,000, divides the $144 sum of the three rates by 4 instead of 3: $144 ÷ 4 = $36, and $36 × 7,500 = $270,000. There are three sales, so the mean is $144 ÷ 3 = $48 per SF, giving $360,000.
Option C: $382,500
Option C, $382,500, uses the highest rate instead of the mean: $51 × 7,500. The mean of the three rates is $48, so the indication is $360,000.
Option D: $1,080,000
Option D, $1,080,000, adds the three rates but does not divide by 3: $144 × 7,500 = $1,080,000. The mean is $144 / 3 = $48 per SF, giving $360,000.
Sum, then divide by count
The mean uses all the values: add them all and divide by how many there are. Three sales means divide by three.
How to use: Use this whenever a question asks for a mean or average unit price.
Exam Tip
A mean must fall between the lowest and highest values; a unit rate outside that range signals a division error.
Common Mistakes to Avoid
- -Adding the rates without dividing by the count
- -Dividing the sum of the rates by the wrong number of sales
- -Using the highest rate when the mean is asked for
- -Confusing the mean with the median
Concept Deep Dive
Analysis
This question tests calculating a mean unit price and applying it to the subject's area. Add the three per-square-foot indications and divide by the number of sales, three, to get the mean. Then multiply that rate by the subject's 7,500 square feet.
Background Knowledge
The arithmetic mean is the sum of values divided by the number of values. In land valuation, a mean unit price from comparable sales can be applied to the subject's units when the sales are similar and cash equivalent. Appraisers also consider the range and reliability of each indication rather than relying on an average alone.
Real-World Application
An appraiser has three recent, similar residential lot sales with closely grouped prices per square foot. After confirming each was cash equivalent, the appraiser uses the mean rate as a check against the reconciled unit value for the subject lot.
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Previous Question
A comparable vacant site with 4,000 buildable square feet sold for $480,000. The subject site has 2,800 buildable square feet and is otherwise matched to the comparable. Both buildable-area figures reflect all binding restrictions. Based on price per buildable (FAR) square foot, what is the indicated land value?
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In a built-up neighborhood, relevant vacant sales are unavailable, but reliable competitive improved sales and credible improvement-contribution or land-ratio evidence exist. Which alternatives can estimate the land component from those improved sales?