An appraiser assigns reliability weights of 2, 3, 1 and 2 to sales at $195,000, $240,000, $270,000 and $330,000, respectively. What is the weighted mean price, to the nearest dollar?
Correct Answer
D) $255,000
195000×2 + 240000×3 + 270000×1 + 330000×2=2040000; total weight=8. Weighted mean=2040000/8=255000, rounded to $255,000. These weights are assigned for the calculation and are not universally appropriate appraisal weights.
Why This Is the Correct Answer
Option D is correct because $195,000 × 2 + $240,000 × 3 + $270,000 × 1 + $330,000 × 2 = $390,000 + $720,000 + $270,000 + $660,000 = $2,040,000, and the weights total 2 + 3 + 1 + 2 = 8. Dividing gives $2,040,000 / 8 = $255,000.
Why the Other Options Are Wrong
Option A: $258,750
Option A, $258,750, is the unweighted mean: ($195,000 + $240,000 + $270,000 + $330,000) / 4 = $1,035,000 / 4 = $258,750. It ignores the weights; the weighted mean is $2,040,000 / 8 = $255,000.
Option B: $510,000
Option B, $510,000, divides the weighted sum by the 4 prices instead of the total weight of 8: $2,040,000 / 4 = $510,000. That is above the highest price, which a weighted mean with positive weights cannot be; the correct result is $2,040,000 / 8 = $255,000.
Option C: $2,040,000
Option C, $2,040,000, is only the weighted sum of price × weight. It must be divided by the total weight of 8 to give $255,000.
Divide by weight total
The denominator of a weighted mean is the sum of the weights, not the number of items.
How to use: Use this to avoid dividing the weighted sum by the count of prices.
Exam Tip
Check that your answer lies between the lowest and highest prices; a weighted mean outside that range means the wrong denominator was used.
Common Mistakes to Avoid
- -Taking a simple average and ignoring the weights
- -Dividing the weighted sum by 4 instead of the total weight of 8
- -Reporting the weighted sum as the answer
Concept Deep Dive
Analysis
This question tests computing a weighted mean with assigned weights. Multiply each price by its weight, sum the products and divide by the total weight, not by the number of prices. Here $2,040,000 / 8 = $255,000.
Background Knowledge
A weighted average adjusts each value by a factor reflecting its relative importance in the whole. With positive weights, the result lies between the lowest and highest values. The weights here are assigned for the calculation only, not as a recommended appraisal weighting.
Real-World Application
A reviewer checks how an appraiser reconciled four comparable indications using stated weights of 2, 3, 1 and 2. Recomputing the weighted sum and dividing by 8 confirms the $255,000 indication reported.
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