Neighborhood closed sales and their list prices: Sale 1 sold for $485,000 (listed $500,000); Sale 2 sold for $441,000 (listed $450,000); Sale 3 sold for $456,000 (listed $480,000); Sale 4 sold for $408,000 (listed $425,000). What mean sale-to-list ratio is indicated (sale price ÷ list price for each sale, then average)? Use the indicated individual-ratio arithmetic mean, not the ratio of price totals.
Correct Answer
B) 96.5 percent
Individual ratios=485000/500000=.97;441000/450000=.98;456000/480000=.95;408000/425000=.96; mean=(.97+.98+.95+.96)/4×100=96.5%. This is the numerical result under the stated definitions, not an automatic market-condition or property-value conclusion. Common errors: reporting the average discount instead of the ratio gives 3.5 percent; inverting the mean ratio gives 103.6 percent; dividing by 3 instead of 4 gives 128.7 percent.
Why This Is the Correct Answer
Option B is correct because the individual ratios are $485,000 / $500,000 = 0.97, $441,000 / $450,000 = 0.98, $456,000 / $480,000 = 0.95 and $408,000 / $425,000 = 0.96. Their mean is (0.97 + 0.98 + 0.95 + 0.96) / 4 = 0.965, or 96.5%. This is the numerical result under the stated definitions, not by itself a conclusion about market conditions.
Why the Other Options Are Wrong
Option A: 3.5 percent
Option A, 3.5 percent, reports the average discount instead of the ratio: (1 - 0.965) x 100 = 3.5. The question asks for the sale-to-list ratio itself, which is (0.97 + 0.98 + 0.95 + 0.96) / 4 x 100 = 96.5%.
Option C: 103.6 percent
Option C, 103.6 percent, inverts the mean ratio: 4 / (0.97 + 0.98 + 0.95 + 0.96) x 100 = 103.6. That gives list-to-sale instead of sale-to-list; the correct mean is 3.86 / 4 x 100 = 96.5%.
Option D: 128.7 percent
Option D, 128.7 percent, divides the sum of four ratios by 3 instead of 4: 3.86 / 3 x 100 = 128.7. There are four sales, so the correct mean is 3.86 / 4 x 100 = 96.5%.
Ratio each, then average
Divide each sale by its own list price first, then average the ratios across all sales.
How to use: Use this order of operations whenever a question asks for the mean of individual sale-to-list ratios.
Exam Tip
Count the sales before averaging, and remember a sale-to-list ratio below 100% means sales closed under asking.
Common Mistakes to Avoid
- -Reporting the average discount instead of the ratio
- -Inverting the ratio to list price over sale price
- -Dividing by the wrong number of sales
Concept Deep Dive
Analysis
This question tests computing a mean sale-to-list ratio from individual sales. Each sale's ratio is its sale price divided by its list price, and the four ratios are then averaged. The ratios are 0.97, 0.98, 0.95 and 0.96, so the mean is 3.86 / 4 = 0.965, or 96.5%.
Background Knowledge
The sale-to-list price ratio shows how closely sale prices track asking prices and is one indicator of market strength. Form 1004MC reports a median sale price as a percentage of list price, while this exercise uses the mean of individual ratios. The method should be stated, because the mean of ratios, the median and the ratio of totals can give different results.
Real-World Application
An appraiser reviews four recent neighborhood sales and computes a mean sale-to-list ratio of 96.5%, showing homes are selling a few percent below asking. Combined with days-on-market data, this supports describing the market as balanced to slightly favoring buyers.
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