Three recent closed sales took 26, 30, and 34 days from contract to close. What is the mean contract-to-close period?
Correct Answer
A) 30 days
Mean = (26 + 30 + 34)/3 = 90/3 = 30 days. Use the same population, period and price/listing definition throughout. Common errors: dividing by 2 instead of 3 gives 45 days; reporting the total days instead of the mean gives 90 days; reporting the longest period gives 34 days.
Why This Is the Correct Answer
Option A is correct because the mean equals (26 + 30 + 34) / 3 = 90 / 3 = 30 days. All three sales are included and the total is divided by the number of sales. The result describes the average contract-to-close period for the sample.
Why the Other Options Are Wrong
Option B: 34 days
Option B, 34 days, simply reports the longest period in the sample. The mean averages all three values: 90 / 3 = 30 days.
Option C: 45 days
Option C, 45 days, comes from dividing the total by 2 instead of 3: 90 / 2 = 45. There are three sales, so the mean is 90 / 3 = 30 days.
Option D: 90 days
Option D, 90 days, reports the total of 26 + 30 + 34 without dividing by the number of sales. The mean is 90 / 3 = 30 days.
Add Them, Count Them, Divide
For a mean, add all the values, count how many there are, and divide the sum by that count.
How to use: Use these three steps to avoid dividing by the wrong number or stopping at the total.
Exam Tip
A quick check: the mean of a set must fall between its lowest and highest values, which rules out 45 and 90 here.
Common Mistakes to Avoid
- -Dividing by the wrong count
- -Reporting the total instead of the average
- -Reporting the maximum value as the average
Concept Deep Dive
Analysis
This question tests computing a simple arithmetic mean from a small sample. The mean is the sum of the values divided by the number of values: (26 + 30 + 34) / 3. The distractors come from using the wrong divisor, reporting the total, or reporting a single value.
Background Knowledge
The arithmetic mean is the sum of observations divided by their count. Market statistics like days on market or contract-to-close time are usually summarized with a mean or median. The sample should use the same population, period and definitions throughout to be meaningful.
Real-World Application
An appraiser notes that three recent comparable sales took 26, 30 and 34 days from contract to close. The 30-day average helps the appraiser estimate approximate contract dates for other comparables whose contract dates are not reported, which matters when judging whether a market conditions adjustment is needed.
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A comparable sold for $350,000. The buyer made a $70,000 down payment and took a $280,000 loan, and the seller paid 2 points on that loan to buy down the buyer's rate. The seller also paid a 6% brokerage commission. Market analysis shows the price rose by the full amount of the points. What is the cash-equivalent sale price?
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For the same closed-sale sample, the median sale price is $408,000 and median final list price is $425,000. What is the ratio of these two medians? This is not necessarily the median of individual sale/list ratios.