Value indications of $720,000, $750,000 and $780,000 receive weights of 20%, 55% and 25%, respectively. What is the weighted indication?
Correct Answer
C) $751,500
Multiply each indication by its assigned weight and sum: $720,000 × 0.2 + $750,000 × 0.55 + $780,000 × 0.25 = $751,500. These weights are given, not prescribed by property type.
Why This Is the Correct Answer
Option C is correct because multiplying each indication by its assigned weight and summing gives $751,500: $720,000 × 0.20 = $144,000; $750,000 × 0.55 = $412,500; $780,000 × 0.25 = $195,000; total $751,500. The weights sum to 100%, so no further division is needed.
Why the Other Options Are Wrong
Option A: $720,000
Option A is wrong because $720,000 is simply the first indication, which carries only a 20% weight. Using it alone ignores the other 80% of the weighting; the correct weighted figure is $144,000 + $412,500 + $195,000 = $751,500.
Option B: $750,000
Option B is wrong because $750,000 is the simple unweighted average, ($720,000 + $750,000 + $780,000) ÷ 3 = $750,000, and also just the middle indication. Applying the stated weights instead gives $751,500.
Option D: $760,500
Option D, $760,500, swaps the second and third weights: $720,000 × 0.20 + $750,000 × 0.25 + $780,000 × 0.55 = $144,000 + $187,500 + $429,000 = $760,500. The 55% weight belongs to $750,000 and the 25% weight to $780,000, which gives $751,500.
Multiply, then add
For a weighted average, multiply each value by its own weight first, then add the products together.
How to use: Use this whenever a question supplies percentage weights for several indications.
Exam Tip
Check that the weights add to 100% and that each weight sits next to its own indication before summing. If an answer equals the simple average, it probably ignored the weights.
Common Mistakes to Avoid
- -Using the simple average instead of applying the weights
- -Attaching a weight to the wrong indication
- -Treating the stated weights as rules for a property type
Concept Deep Dive
Analysis
This question tests the weighted-average calculation with stated weights. Multiply each indication by its own weight, in the stated order, and add the products. The weights are stated in the facts, so the task is arithmetic, not a judgment about which approach deserves weight.
Background Knowledge
A weighted average multiplies each value by its weight and adds the results; when the weights total 100%, that sum is the weighted average. In appraisal, a weighted average may be used in reconciliation when the weights are supported and explained. The final opinion should not be derived by a purely formulaic averaging approach.
Real-World Application
An appraiser who has explained why sales comparison deserves most weight presents a weighted reconciliation table for a reviewer. The table shows each indication, its supported weight and the product, so the reviewer can verify the arithmetic and the reasoning.
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