Three improved sales show site values of $90,000, $110,000 and $96,000 against prices of $360,000, $400,000 and $400,000. Using the median site-to-total ratio, what site value does allocation indicate for a subject valued at $450,000?
Correct Answer
B) $112,500
The ratios are 0.25, 0.275 and 0.24; the median is 0.25. Allocation applies the ratio to the subject’s total value: $450,000 × 0.25 = $112,500. The mean ratio (0.255) gives $114,750.
Why This Is the Correct Answer
Option B is correct because the ratios are $90,000/$360,000 = 0.25, $110,000/$400,000 = 0.275 and $96,000/$400,000 = 0.24, and the median of 0.24, 0.25 and 0.275 is 0.25. Applying it to the subject gives $450,000 × 0.25 = $112,500. Allocation applies the ratio to the subject's total value to estimate site value.
Why the Other Options Are Wrong
Option A: $110,000
Option A, $110,000, is one comparable's site value, not a ratio applied to the subject. The median ratio of 0.25 applied to $450,000 gives $112,500.
Option C: $114,750
Option C, $114,750, uses the mean ratio instead of the median: (0.25 + 0.275 + 0.24) ÷ 3 = 0.255, and $450,000 × 0.255 = $114,750. The question asks for the median, 0.25, which gives $112,500.
Option D: $123,750
Option D, $123,750, uses the highest ratio: $450,000 × 0.275 = $123,750. The median ratio is 0.25, so the correct result is $112,500.
Sort first, then middle
To find a median, sort the ratios from low to high and take the middle one: 0.24, 0.25, 0.275 gives 0.25.
How to use: Use this whenever a question asks for the median of a small set of figures.
Exam Tip
Compute each ratio, sort them, and check whether the question asks for the median or the mean, since both often appear among the choices.
Common Mistakes to Avoid
- -Using the mean ratio when the median is required
- -Taking the median of the site values instead of the ratios
- -Forgetting to sort the ratios before picking the middle one
Concept Deep Dive
Analysis
This question tests the allocation method using a ratio derived from several sales. Each sale's site value is divided by its price to find a site-to-total ratio, the median ratio is selected, and that ratio is applied to the subject's total value. Distinguishing median from mean and from the highest ratio is the key.
Background Knowledge
Allocation estimates site value as a share of total property value, using ratios observed in comparable sales. It is most useful when vacant land sales are scarce. The median is the middle value of a sorted set and is less affected by extreme values than the mean.
Real-World Application
In a built-up suburb with no recent vacant lot sales, an appraiser studies three improved sales where site values were estimated. The site-to-total ratios cluster around 25%, so the appraiser applies 0.25 to the subject's $450,000 value to indicate a $112,500 site value.
More Land/Site Questions
How should an appraiser account for a site's access to public sewer compared with competing sites that require septic systems?
Which fact, if supported by competitive-market evidence, most directly supports a unit-price premium for an otherwise comparable site?
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Using the allocation method, market evidence supports a typical land-to-total-property-value ratio of 28% for similar improved properties in the subject’s location. An improved comparable sold for $825,000. What land (site) contribution is indicated by applying that ratio?
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