Vacant land may be valued by a multi-comparable median unit price ($/SF of site) applied to the subject’s site area. Five similar vacant comps support unit prices of $34, $36, $38, $40, and $43 per square foot. Subject contains 15,000 SF. What indicated land value by median $/SF results?
Correct Answer
B) $570,000
Median of 34, 36, 38, 40, 43 is $38/SF; land = 15,000 SF × $38/SF = $570,000. The indicated value is $570,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: using the mean instead of the median gives $573,000; using the lowest unit rate gives $510,000; using the highest unit rate gives $645,000.
Why This Is the Correct Answer
Option B is correct because the median of $34, $36, $38, $40 and $43 is the middle value, $38 per SF. Multiplying by the subject's size gives 15,000 × $38 = $570,000. The question specifically asks for the median, not the mean.
Why the Other Options Are Wrong
Option A: $510,000
Option A, $510,000, uses the lowest rate: $34 × 15,000. The median is $38, giving 15,000 × $38 = $570,000.
Option C: $573,000
Option C, $573,000, uses the mean instead of the median: ($34 + $36 + $38 + $40 + $43) / 5 = $38.20, and $38.20 × 15,000 = $573,000. The question asks for the median, $38, which gives $570,000.
Option D: $645,000
Option D, $645,000, uses the highest rate: $43 × 15,000. The median of the five rates is $38, so the indication is $570,000.
Median sits in the middle
Like the median strip down the middle of a highway, the median is the middle value once the numbers are in order.
How to use: Use this to tell median from mean when a question lists several unit prices.
Exam Tip
Put the values in order before picking the median, and do not average them unless the question asks for the mean.
Common Mistakes to Avoid
- -Computing the mean when the median is asked for
- -Picking the middle value without sorting the data first
- -Applying the high or low rate instead of a central value
Concept Deep Dive
Analysis
This question tests finding the median unit price and applying it to the subject's area. With five values listed in order, the median is the middle (third) value, $38. That rate is multiplied by the subject's 15,000 square feet.
Background Knowledge
The median is the middle value of a data set arranged in order; with an even count it is the average of the two middle values. It is less affected by an extreme high or low value than the mean. Appraisers may use measures of central tendency as a check, but reconciliation still weighs each comparable's reliability.
Real-World Application
An appraiser has five vacant lot sales, one of which sold at a noticeably higher price per square foot. Using the median unit price as a check limits the pull of that one high sale while the appraiser investigates why it sold higher.
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