Vacant land may be valued by a multi-comparable mean unit price ($/front foot) applied to the subject’s street frontage. Four similar vacant comps support unit prices of $2,500, $2,700, $2,900, and $3,100 per front foot. Subject has 160 front feet. What indicated land value by mean $/FF results?
Correct Answer
B) $448,000
Mean = ($2,500 + $2,700 + $2,900 + $3,100)/4 = $2,800/front foot; value = 160 × $2,800 = $448,000. The indicated result is $448,000. Common errors: dividing the sum of the rates by 5 instead of 4 gives $358,400; using the highest unit rate gives $496,000; dividing the sum of the rates by 3 instead of 4 gives $597,333.
Why This Is the Correct Answer
Option B is correct because the mean is ($2,500 + $2,700 + $2,900 + $3,100) ÷ 4 = $2,800 per front foot. Multiplying by 160 front feet gives 160 × $2,800 = $448,000.
Why the Other Options Are Wrong
Option A: $358,400
Option A, $358,400, divides the $11,200 sum by 5 instead of 4 ($2,240 × 160). There are four comparables, so the mean is $2,800 and the value is $448,000.
Option C: $496,000
Option C, $496,000, uses the highest unit rate ($3,100 × 160) instead of the mean. The mean of $2,800 gives $448,000.
Option D: $597,333
Option D, $597,333, divides the sum of $11,200 by 3 instead of 4 ($3,733.33 × 160). There are four comparables, so the mean is $2,800 and the value is $448,000.
Divide by the count
A mean is the sum divided by how many items you added. Four comparables means divide by four.
How to use: Use this to check the divisor in any averaging problem.
Exam Tip
The correct answer for a mean should fall between the values from the lowest and highest rates.
Common Mistakes to Avoid
- -Dividing by the wrong number of comparables
- -Using the lowest or highest rate instead of the mean
- -Multiplying by depth instead of frontage
Concept Deep Dive
Analysis
This question tests calculating a mean unit price from several comparables and applying it to the subject's frontage. Add the four unit prices, divide by four, and multiply by the subject's front feet. The distractors use the highest rate or a wrong divisor.
Background Knowledge
Price per front foot is a unit of comparison used where street frontage drives value, such as commercial strips or waterfront lots. A mean of several comparables' unit prices is one measure of central tendency, and the appraiser considers whether the comparables are similar enough for the mean to be meaningful.
Real-World Application
An appraiser values a commercial lot on a busy corridor where buyers price land by street frontage. Four similar lot sales produce a range of front-foot prices, and the appraiser applies their mean to the subject's 160 feet of frontage.
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