For the same competitive closed-sale sample, median final list price is $480,000 and median sale price is $456,000. What is the difference between those medians divided by the list-price median, as a percentage? This need not equal the mean or median of individual negotiation discounts.
Correct Answer
A) 5.0 percent
Relative gap=($480,000−$456,000)/$480,000×100=5%. This is the numerical result under the stated definitions, not an automatic market-condition or property-value conclusion. Common errors: dividing by the sale-price median instead of the list-price median gives 5.3 percent; reporting the sale-to-list percentage instead of the discount gives 95.0 percent; inverting the ratio (list ÷ sale) gives 105.3 percent.
Why This Is the Correct Answer
Option A is correct because the difference between the medians is $480,000 - $456,000 = $24,000, and $24,000 / $480,000 x 100 = 5.0 percent. The question defines the base as the list-price median, so the list figure goes in the denominator. This is the numerical result under the stated definitions, not a conclusion about market conditions or property value.
Why the Other Options Are Wrong
Option B: 5.3 percent
Option B, 5.3 percent, comes from dividing by the sale-price median instead of the list-price median: ($480,000 - $456,000) / $456,000 x 100 = 5.3 percent. The correct base is the list-price median, giving $24,000 / $480,000 x 100 = 5.0 percent.
Option C: 95.0 percent
Option C, 95.0 percent, reports the sale-to-list percentage instead of the gap: $456,000 / $480,000 x 100 = 95.0 percent. The question asks for the difference divided by the list median, which is ($480,000 - $456,000) / $480,000 x 100 = 5.0 percent.
Option D: 105.3 percent
Option D, 105.3 percent, inverts the ratio by dividing list by sale: $480,000 / $456,000 x 100 = 105.3 percent. The question asks for the difference between the medians divided by the list median, which is $24,000 / $480,000 x 100 = 5.0 percent.
Base Goes Below
The figure named as the base, here the list-price median, goes in the denominator. Subtract first, then divide by the base.
How to use: Use this reminder whenever a percentage question names what the difference is divided by.
Exam Tip
Read the stem for the exact denominator and for whether it asks for a gap or a ratio. Answer choices often include the ratio and the inverted ratio as traps.
Common Mistakes to Avoid
- -Dividing the difference by the sale-price median instead of the list-price median
- -Reporting the sale-to-list ratio when the question asks for the gap
- -Assuming the gap between medians equals the median of individual discounts
Concept Deep Dive
Analysis
This question tests calculating the relative gap between two sample medians, using the list-price median as the base. The correct calculation is ($480,000 - $456,000) / $480,000 x 100 = 5 percent. The distractors come from using the wrong base, reporting the sale-to-list ratio instead of the gap, or inverting the ratio.
Background Knowledge
Market conditions analysis often reports median sale price, median list price and median sale price as a percentage of list price. A gap computed from two sample medians is not necessarily the same as the mean or median of individual sale-to-list discounts. Appraisers use these figures as indicators and interpret them alongside other market evidence.
Real-World Application
An appraiser preparing a market conditions analysis finds a median list price of $480,000 and a median sale price of $456,000 for competing closed sales. She computes a 5 percent gap relative to the list median and reports that the median sale price is 95 percent of the median list price. She notes that this gap is not the same as the average discount on individual sales.
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