Vacant land may be valued by a multi-comparable median unit price ($/acre) applied to the subject’s acreage. Five similar vacant comps support unit prices of $88,000, $95,000, $98,000, $102,000, and $110,000 per acre. Subject contains 7.5 acres. What indicated land value by median $/acre results?
Correct Answer
B) $735,000
Median of $88,000, $95,000, $98,000, $102,000, $110,000 is $98,000/acre; subject = 7.5 × $98,000 = $735,000. The indicated result is $735,000. Common errors: using the mean instead of the median gives $739,500; using the lowest unit rate gives $660,000; using the highest unit rate gives $825,000.
Why This Is the Correct Answer
Option B is correct because the median of $88,000, $95,000, $98,000, $102,000 and $110,000 per acre is the middle value, $98,000. Multiplying 7.5 acres by $98,000 gives $735,000. The question asks for the median, not the mean or an extreme value, so $735,000 is the indicated land value.
Why the Other Options Are Wrong
Option A: $660,000
Option A, $660,000, comes from using the lowest unit rate: 7.5 × $88,000 = $660,000. The question calls for the median rate, and 7.5 × $98,000 = $735,000.
Option C: $739,500
Option C, $739,500, uses the mean instead of the median: ($88,000 + $95,000 + $98,000 + $102,000 + $110,000) ÷ 5 = $98,600, and 7.5 × $98,600 = $739,500. The median is $98,000, so the correct result is 7.5 × $98,000 = $735,000.
Option D: $825,000
Option D, $825,000, comes from using the highest unit rate: 7.5 × $110,000 = $825,000. The median rate of $98,000 gives 7.5 × $98,000 = $735,000.
Median sits in the middle
Like the median strip in the middle of a highway, the median is the value in the middle once the numbers are lined up from low to high.
How to use: Use this when a question asks for a median: sort the values first, then pick the middle one.
Exam Tip
Read whether the question asks for the mean or the median, because distractors are often built from the other measure. With an odd number of values, the median is simply the middle value after sorting.
Common Mistakes to Avoid
- -Averaging the unit prices when the question asks for the median
- -Forgetting to sort the values before selecting the middle one
- -Applying the lowest or highest comparable rate instead of the median
Concept Deep Dive
Analysis
This question tests whether you can find the median of a set of unit prices and apply it to the subject's size. Put the five per-acre prices in order and pick the middle value, which is $98,000. Then multiply by the subject's 7.5 acres to reach the indicated land value.
Background Knowledge
Vacant land is often compared using units of comparison such as price per acre, price per square foot or price per buildable unit. The median is the middle value of an ordered set and is less affected by unusually high or low sales than the mean. Choosing the measure of central tendency is part of reconciling unit-price evidence.
Real-World Application
An appraiser valuing a 7.5-acre rural parcel finds five recent vacant sales with per-acre prices that spread from $88,000 to $110,000. To limit the influence of the highest and lowest sales, she looks at the median rate as one indicator and applies it to the subject's acreage before reconciling with other evidence.
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