Four recent closed sales in the subject’s competitive market have the following sale-to-list ratios (sale price ÷ most recent list price): 0.98, 0.96, 0.98, and 0.97. What is the arithmetic mean sale-to-list ratio for this set (standard appraisal guidance / market analysis of listings and closed sales)?
Correct Answer
C) 0.97 ratio
Mean = (0.98 + 0.96 + 0.98 + 0.97)/4 = 3.89/4 = 0.9725. Use the same population, period and price/listing definition throughout. Common errors: dividing by 3 instead of 4 gives 1.30 ratio; dividing by 5 instead of 4 gives 0.78 ratio; reporting the lowest ratio gives 0.96 ratio.
Why This Is the Correct Answer
Option C is correct because the mean equals (0.98 + 0.96 + 0.98 + 0.97) / 4 = 3.89 / 4 = 0.9725, which rounds to 0.97. All four sales are included and divided by four. The result falls between the lowest and highest ratios, as a mean must.
Why the Other Options Are Wrong
Option A: 0.78 ratio
Option A, 0.78, comes from dividing the total by 5 instead of 4: 3.89 / 5 = 0.78. There are four sales, so the mean is 3.89 / 4 = 0.97.
Option B: 0.96 ratio
Option B, 0.96, is the lowest ratio in the set rather than the mean. Averaging all four gives 3.89 / 4 = 0.97.
Option D: 1.30 ratio
Option D, 1.30, comes from dividing the total by 3 instead of 4: 3.89 / 3 = 1.30. With four sales the mean is 3.89 / 4 = 0.97.
Mean Stays Inside the Range
A mean has to land between the smallest and largest values, here between 0.96 and 0.98.
How to use: Use the range check to eliminate answers like 0.78 and 1.30 immediately.
Exam Tip
After calculating a mean, confirm it lies between the lowest and highest values; anything outside that range used the wrong divisor.
Common Mistakes to Avoid
- -Dividing by the wrong number of sales
- -Reporting the minimum value instead of the mean
- -Mixing original and final list prices in the same set
Concept Deep Dive
Analysis
This question tests computing an arithmetic mean of four ratios. Add 0.98 + 0.96 + 0.98 + 0.97 = 3.89, then divide by 4 to get 0.9725, which rounds to 0.97. The distractors come from dividing by the wrong count or reporting one of the values.
Background Knowledge
The sale-to-list ratio compares a sale price to its most recent list price. Averaging individual ratios across a set of sales gives a mean ratio, which is one way to summarize how close sales come to asking prices. Medians and other measures of location can also be used, and the data should use consistent definitions.
Real-World Application
An appraiser reviews four competing sales that closed at 98, 96, 98 and 97 percent of their final list prices. The average of about 97 percent helps the appraiser describe typical negotiation from list price in the market conditions analysis.
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