To gauge how much negotiation is occurring in a market, an appraiser reviews three recently closed sales with sale-to-list price ratios of 0.95, 0.98, and 1.01. What is the median sale-to-list ratio?
Correct Answer
B) 0.98 ratio
Ordered ratios 0.95,0.98,1.01; median is the middle observation 0.98. Use the same population, period and price/listing definition throughout. Common errors: reporting the lowest ratio gives 0.95 ratio; reporting the highest ratio gives 1.01 ratio; dividing the sum by 2 gives 1.47 ratio.
Why This Is the Correct Answer
Option B is correct because the ordered ratios are 0.95, 0.98 and 1.01, and the median is the middle observation, 0.98. One ratio lies below it and one above it.
Why the Other Options Are Wrong
Option A: 0.95 ratio
Option A is wrong because 0.95 is the lowest ratio, not the middle one. The median of 0.95, 0.98 and 1.01 is 0.98.
Option C: 1.01 ratio
Option C is wrong because 1.01 is the highest ratio, not the middle one. The median of 0.95, 0.98 and 1.01 is 0.98.
Option D: 1.47 ratio
Option D is wrong because 1.47 comes from dividing the sum by 2: (0.95 + 0.98 + 1.01) / 2 = 2.94 / 2 = 1.47. The median is simply the middle ordered value, 0.98.
Line them up, take middle
To find a median, line the values up from low to high and take the one in the middle.
How to use: Use this two-step routine on any median question with a small data set.
Exam Tip
A median cannot exceed the largest value in the set, so an answer like 1.47 from ratios near 1.00 can be eliminated at once.
Common Mistakes to Avoid
- -Reporting the lowest or highest ratio as the median
- -Dividing the sum by the wrong number
- -Confusing a ratio below 1 with a quantified concession amount
Concept Deep Dive
Analysis
This question tests finding the median of three ordered values. With an odd count of three, the median is the middle observation once the ratios are ordered, not the lowest, highest or a miscalculated average.
Background Knowledge
The sale-to-list price ratio compares the sale price with the list price and can indicate how much negotiation is occurring. Market conditions analysis commonly reports the median ratio because it resists distortion from a few unusual sales. Ratios should use a consistent population, period and list-price definition.
Real-World Application
An appraiser reviews three recent competing sales that closed at 95, 98 and 101 percent of list price. The median ratio of 0.98 suggests buyers are negotiating modestly below list, which the appraiser weighs with other market indicators.
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