Four comparable sales, after all adjustments, indicate $148, $152, $151 and $149 per square foot. The subject contains 1,850 square feet. Using the mean of these rates, what is the indicated value of the subject?
Correct Answer
B) $277,500
(148 + 152 + 151 + 149) / 4 = 150; 150 × 1850 = 277500. Common errors: using the lowest rate gives $273,800; using the highest rate gives $281,200; dividing the sum of the rates by 3 instead of 4 gives $370,000.
Why This Is the Correct Answer
Option B is correct because the four rates sum to $148 + $152 + $151 + $149 = $600, and $600 ÷ 4 = $150 per square foot. Applying that to the subject gives $150 × 1,850 = $277,500.
Why the Other Options Are Wrong
Option A: $273,800
Option A, $273,800, uses the lowest rate instead of the mean: $148 × 1,850. The mean rate is $150, which gives $277,500.
Option C: $281,200
Option C, $281,200, uses the highest rate instead of the mean: $152 × 1,850. The mean rate is $150, which gives $277,500.
Option D: $370,000
Option D, $370,000, divides the $600 sum by 3 instead of 4, giving $200 per square foot and $200 × 1,850 = $370,000. There are four rates, so the mean is $150 and the indication is $277,500.
Count the comps you sum
The divisor for a mean is the number of values you added, so four rates means divide by four.
How to use: Use this on any averaging question to avoid a wrong divisor.
Exam Tip
A quick check is that the mean must fall between the lowest and highest values; a result far outside that range signals a divisor error.
Common Mistakes to Avoid
- -Dividing by the wrong number of values
- -Using only the highest or lowest rate
- -Applying the mean to the wrong square footage
Concept Deep Dive
Analysis
This question tests computing a simple mean of unit rates and applying it to the subject's size. Add the four rates, divide by four, then multiply by 1,850 square feet. The rates are already adjusted, so no further adjustment is needed.
Background Knowledge
Units of comparison, such as price per square foot, let the appraiser state each sale price on a common basis. Once the unit rates have been made comparable, a measure of central tendency can be applied to the subject's units. In real assignments appraisers reconcile rates using judgment rather than relying only on a simple average.
Real-World Application
An appraiser has four adjusted comparables between $148 and $152 per square foot. The mean of $150 applied to a 1,850 square foot home gives a $277,500 indication, which is then weighed against other evidence.
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