Seven recent closed sales in the subject’s competitive market have sale-to-list ratios (sale price ÷ most recent list price) of 0.95, 0.97, 0.98, 0.99, 1.00, 1.02 and 1.04. What is their arithmetic mean sale-to-list ratio, rounded to three decimal places?
Correct Answer
A) 0.993
The seven ratios sum to 6.95, and 6.95 ÷ 7 = 0.9929…, which rounds to 0.993. The median is 0.990 and the midrange (0.95 + 1.04) ÷ 2 is 0.995; both are different statistics. 0.992 truncates instead of rounding. The mean is a descriptive market statistic, not by itself a market-condition conclusion or a value adjustment.
Why This Is the Correct Answer
Option A is correct because the seven ratios sum to 6.95, and 6.95 divided by 7 equals 0.992857, which rounds to 0.993. The digit after the third decimal place is 8, so the third decimal rounds up from 2 to 3. This mean is a descriptive statistic and is not by itself a market-conditions conclusion or a value adjustment.
Why the Other Options Are Wrong
Option B: 0.990
Option B, 0.990, is the median, the middle (fourth) value of the seven ordered ratios, not the arithmetic mean. The mean is 6.95 divided by 7, or 0.992857, which rounds to 0.993.
Option C: 0.995
Option C, 0.995, is the midrange, computed as (0.95 + 1.04) divided by 2. The question asks for the mean, which is 6.95 divided by 7, or about 0.993.
Option D: 0.992
Option D, 0.992, comes from truncating 0.992857 instead of rounding it. Because the next digit is 8, correct rounding gives 0.993.
Mean adds all, median middles
The mean adds all the values and divides by the count; the median picks the middle value once the data are sorted.
How to use: Use this to check that you computed the statistic the question actually names.
Exam Tip
When an answer must be rounded, look at the next digit before choosing; a truncated figure is a common distractor.
Common Mistakes to Avoid
- -Reporting the median when the mean is requested
- -Truncating instead of rounding the final figure
- -Averaging only the highest and lowest values
Concept Deep Dive
Analysis
This question tests calculating an arithmetic mean and rounding it correctly. Add all seven ratios, divide by seven, and round to three decimal places. The distractors are other statistics from the same data set, such as the median and midrange, or a truncated result.
Background Knowledge
Mean, median and midrange are different measures of central tendency. The mean uses all of the values, the median is the middle value of an ordered set, and the midrange uses only the highest and lowest values. Market condition reports often use medians, so appraisers must be clear about which statistic they are reporting.
Real-World Application
An appraiser reviewing seven recent sales in a subdivision computes the average sale-to-list ratio to describe how close homes are selling to list price. The appraiser reports the mean along with the median and notes that the statistic alone does not establish a market-conditions adjustment.
More Market Questions
In market area analysis, what characteristic distinguishes a district from a neighborhood?
Under USPAP Standards Rule 1-3(a), which item must an appraiser identify and analyze when necessary for credible results in a market value assignment?
How does the Fannie Mae Selling Guide define a neighborhood?
Several homes in a neighborhood are vacant and boarded up. Which market force does Fannie Mae classify this as?
Infrastructure investment such as a new interchange typically affects nearby land by:
A city raises property tax rates and tightens building regulations. Which market force does Fannie Mae classify these as?
An appraiser believes, without market evidence, that a nearby group home lowers values. What does Fannie Mae require?
Which three categories are used to report the supply of properties in a Fannie Mae neighborhood section?
An appraiser is asked for a retrospective value opinion as of three years ago. When must the appraiser meet the Competency Rule?
Can mixed land uses in a residential neighborhood ever enhance home values, according to Fannie Mae?
People Also Study
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Income Approach
8.2% of exam
Previous Question
An investor will pay more for a building next to its existing headquarters than other buyers would. The value of the building to that particular investor is called:
Next Question
Other conditions equal, net comparable apartments available for rent increase while effective demand for that segment remains unchanged. What competitive pressure on new-lease asking rents is most likely?