Three closed competitive sales have sale-to-list ratios of 0.96, 0.98, and 1.00. What is the mean sale-to-list ratio?
Correct Answer
B) 0.98
Mean = (0.96 + 0.98 + 1.00)/3 = 2.94/3 = 0.98. Keep the stated numerator, denominator and units distinct. Common errors: dividing by 2 instead of 3 gives 1.47; not dividing the sum by the count gives 2.94; reporting the lowest ratio gives 0.96.
Why This Is the Correct Answer
Option B is correct because the mean is the sum of the ratios divided by their count: (0.96 + 0.98 + 1.00) / 3 = 2.94 / 3 = 0.98. A mean ratio near 0.98 indicates sales closed, on average, slightly below list price.
Why the Other Options Are Wrong
Option A: 0.96
Option A, 0.96, is just the lowest of the three ratios. Reporting one observation ignores the other two; the mean is 2.94 / 3 = 0.98.
Option C: 1.47
Option C, 1.47, results from dividing the sum by 2 instead of 3: 2.94 / 2 = 1.47. There are three sales, so the correct mean is 2.94 / 3 = 0.98.
Option D: 2.94
Option D, 2.94, is the sum of the ratios without dividing by the count: 0.96 + 0.98 + 1.00 = 2.94. Dividing by the three sales gives 0.98.
Add, then divide by count
A mean is a fair share: pool all the values, then split them evenly among the number of items.
How to use: Use this when averaging ratios, prices or days on market from a small set of sales.
Exam Tip
Check that your answer falls between the lowest and highest values; a mean of ratios between 0.96 and 1.00 cannot be 1.47 or 2.94.
Common Mistakes to Avoid
- -Dividing the sum by the wrong number of observations
- -Forgetting to divide the sum at all
- -Reporting the lowest or highest single ratio as the average
Concept Deep Dive
Analysis
This question tests a simple arithmetic mean of three sale-to-list ratios. Add the ratios and divide by the number of sales. Distractors come from using the wrong divisor, forgetting to divide, or reporting a single observation.
Background Knowledge
Sale-to-list ratios compare closing price with list price and help show negotiating conditions in a market segment. The arithmetic mean is one measure of central tendency; market-conditions forms also report medians, which are less sensitive to extreme values.
Real-World Application
An appraiser reviewing three recent closed sales in a subdivision finds sale-to-list ratios of 96%, 98% and 100%. She notes an average of about 98% and comments that buyers are negotiating modestly below list price.
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