Three comparable sales produce adjusted indications of $288,000, $292,000 and $296,000. In reconciling them, the appraiser weights these indications 50%, 30% and 20%, respectively. What is the weighted indication?
Correct Answer
B) $290,800
288000×0.50+292000×0.30+296000×0.20=290800. Common errors: using an equal mean instead of the assigned weights gives $292,000; applying the weights in reverse order gives $293,200; reporting the most heavily weighted indication gives $288,000.
Why This Is the Correct Answer
Option B is correct because $288,000 × 0.50 = $144,000, $292,000 × 0.30 = $87,600 and $296,000 × 0.20 = $59,200, and these sum to $290,800. The weights are applied in the order given. The result is pulled toward the most heavily weighted indication.
Why the Other Options Are Wrong
Option A: $288,000
Option A, $288,000, simply reports the most heavily weighted indication. The weighted calculation also includes the other two indications and gives $290,800.
Option C: $292,000
Option C, $292,000, is the equal mean: ($288,000 + $292,000 + $296,000) ÷ 3 = $292,000. Using the assigned 50%, 30% and 20% weights gives $290,800.
Option D: $293,200
Option D, $293,200, applies the weights in reverse order: $288,000 × 0.20 + $292,000 × 0.30 + $296,000 × 0.50 = $293,200. Applying them in the stated order gives $290,800.
Multiply, then add
Weighted average equals each value times its weight, all added together, with weights matched in order.
How to use: Use this for any weighted indication question.
Exam Tip
Check that the weights sum to 100% and that your answer falls closest to the most heavily weighted value.
Common Mistakes to Avoid
- -Using a simple average when weights are given
- -Matching weights to the wrong indications
- -Treating a weighted average as a substitute for reasoned reconciliation
Concept Deep Dive
Analysis
This question tests a weighted average calculation with assigned weights. Each adjusted indication is multiplied by its weight, and the products are summed. The arithmetic does not itself justify the weights, which in practice must come from the appraiser's reasoned judgment.
Background Knowledge
Reconciliation weighs indications based on their reliability and relevance. A weighted average can illustrate the result of chosen weights, but the final opinion should not be derived by a formulaic approach such as averaging. The weights must be explained by the appraiser's analysis.
Real-World Application
An appraiser reconciles three adjusted comparables and gives the most weight to the most similar sale. The report explains why each sale received its weight rather than relying on a mechanical average.
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