Vacant land may be valued by a multi-comparable median unit price ($/front foot) applied to the subject’s street frontage. Five similar vacant comps support unit prices of $2,400, $2,600, $2,800, $3,000, and $3,200 per front foot. Subject has 180 front feet. What indicated land value by median $/FF results?
Correct Answer
B) $504,000
Median is $2,800/front foot; 180 front feet × $2,800/front foot = $504,000. The indicated value is $504,000. 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 gives $432,000; adding the five rates and dividing by 4 gives $630,000; averaging two middle values as if the count were even gives $522,000.
Why This Is the Correct Answer
Option B is correct because the median of $2,400, $2,600, $2,800, $3,000 and $3,200 is the middle value, $2,800 per front foot. Applying it gives 180 × $2,800 = $504,000.
Why the Other Options Are Wrong
Option A: $432,000
Option A, $432,000, uses the lowest unit rate: 180 × $2,400 = $432,000. The median rate is $2,800, giving 180 × $2,800 = $504,000.
Option C: $522,000
Option C, $522,000, averages two middle values as if the count were even: ($2,800 + $3,000) ÷ 2 = $2,900, and 180 × $2,900 = $522,000. With five values the median is the single middle value, $2,800, giving $504,000.
Option D: $630,000
Option D, $630,000, adds the five rates and divides by 4: $14,000 ÷ 4 = $3,500, and 180 × $3,500 = $630,000. The median is the middle ordered value, $2,800, giving $504,000.
Odd count, one middle
With an odd number of values there is exactly one middle value; only an even count needs averaging of two.
How to use: Use this to decide whether to pick one middle value or average two.
Exam Tip
Count the values before finding the median; five values means the third in order is the median.
Common Mistakes to Avoid
- -Averaging two middle values when the count is odd
- -Using the lowest rate or a miscounted average as the indication
- -Forgetting to multiply by the subject's frontage
Concept Deep Dive
Analysis
This question tests the median of an odd-numbered set of front-foot prices applied to the subject's frontage. With five values, the median is the third value in order. Multiply it by the subject's 180 front feet.
Background Knowledge
For an odd number of observations, the median is the single middle value; for an even number, it is the average of the two central values. Front-foot pricing is appropriate where frontage drives market value.
Real-World Application
An appraiser values a commercial lot on a busy arterial with 180 feet of frontage. Five competing frontage sales are converted to price per front foot, and she uses the median as a check on her adjusted sales comparison.
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Previous Question
Five cash-equivalent sales of competitive vacant sites indicate $44, $48, $55, $58, and $62 per square foot. The subject site contains 6,400 square feet. Based on the median price per square foot, what is the indicated land value?
Next Question
Plottage (assemblage) value is the increment created when two or more parcels are combined into a larger unit worth more than the sum of the separate parcels, after assemblage costs. Parcel A is worth $320,000 alone and Parcel B is worth $210,000 alone. Combined as one site, market value is $610,000. Direct assemblage costs (legal, demolition of a fence, surveying) total $35,000. What net plottage value results?