An appraiser reports a mean sale price of $327,483.62. What is the difficulty with this?
Correct Answer
B) The figure implies unwarranted precision
Why this is correct: Reporting a mean sale price to the cent ($327,483.62) implies a level of precision that is not justified by the underlying market data, which is inherently imprecise and often rounded. This is a violation of the principle that communicated precision should not exceed the precision of the evidence. Why the other choices are wrong: The mean can be a useful measure to report. There is no rule prohibiting cents in reports. While the median is often more appropriate for skewed data, it is not required to be reported alongside the mean. Exam tip: Avoid spurious precision. Round your statistics to reflect the reliability of your data (e.g., to the nearest hundred or thousand dollars).
Why This Is the Correct Answer
The figure implying unwarranted precision is the difficulty, and the principle is that communicated precision should not exceed what the evidence supports. Rounding to a level that reflects the data's reliability, commonly the nearest hundred or thousand dollars for sale price statistics, communicates the finding honestly and does not invite a reader to over-rely on it. The same discipline applies throughout a report, including adjustment amounts, rates, and the final value opinion, where excessive digits suggest a resolution the analysis cannot deliver. Alongside the rounding, a report presenting central tendency should state the sample size and the period and area the sales came from, so the reader can judge what the statistic describes.
Why the Other Options Are Wrong
Option A: The mean should never be reported at all
The mean is a legitimate and frequently useful statistic, and nothing prohibits reporting it; central tendency measures are ordinary tools in market analysis. The caution about the mean is narrower, that it is pulled by outliers and may misdescribe a skewed distribution, which argues for reporting the median alongside it rather than for suppressing it. Candidates pick this by escalating a caveat into a prohibition.
Option C: Cents are prohibited in appraisal reports
No rule forbids cents in appraisal reports, and cents appear legitimately in places where the underlying quantity really is that precise, such as a contract rent stated in a lease or a per-square-foot figure carried in an intermediate calculation. The problem in the stem is not the presence of cents as a matter of form but that the market data cannot support resolution at that level. This option converts a reasoning principle into a formatting rule.
Option D: The median must be reported alongside it
Reporting the median alongside the mean is often excellent practice, particularly for skewed price distributions, and a candidate who chooses this has a real point about describing a distribution well. It is not a requirement, and it does not address the difficulty the stem raises, since a median reported to the cent would carry exactly the same false precision. The option identifies a good habit rather than the flaw in the figure.
Digits Are a Claim
Every digit you print is a promise that you can tell this number from the one next to it. Sixty-two cents promises you can distinguish this market's average from one a penny different. Round until the promise is one you can keep.
How to use: When a stem shows a figure carried to an implausible number of digits, name the false precision rather than reaching for a prohibition or a formatting rule. Then ask separately whether the statistic chosen fits the distribution, since the mean and median answer different questions.
Exam Tip
Spurious precision questions appear throughout this exam applied to statistics, measurements, adjustments, and value conclusions. The answer is always that the expression outruns the evidence.
Common Mistakes to Avoid
- -Carrying the precision of a calculator display into the report as though it were information
- -Reporting a mean for a visibly skewed set of sales without also giving the median
- -Presenting a statistic without the sample size, period, and market area that define what it describes
Concept Deep Dive
Analysis
Precision and accuracy are different properties of a number, and reporting a statistic to the cent confuses them. Accuracy is how close a figure is to the truth; precision is how finely it is expressed. A mean computed from a set of sale prices will always come out of the arithmetic with as many decimal places as you care to keep, but those digits are an artifact of division rather than information about the market, because the inputs themselves are prices produced by negotiation and rounded by convention, and the sample is one of many samples that could have been drawn. Expressing the result as three hundred twenty-seven thousand four hundred eighty-three dollars and sixty-two cents tells a reader, implicitly, that the appraiser can distinguish this market's central tendency from one a dollar higher, which no data supports. There is a second dimension worth noting: the mean is sensitive to extreme values, so in a skewed set of sale prices the median often describes the typical transaction better, and an appraiser reporting central tendency should be thinking about which measure fits the distribution as well as how finely to express it.
Background Knowledge
You need to know the difference between precision and accuracy, and that the number of digits reported implies a resolution the underlying data must be able to support. You should know that the mean is sensitive to extreme values while the median better describes central tendency in a skewed distribution, and that reporting both is often informative. You also need to know that statistics presented in a report should be accompanied by sample size, time period, and market area so a reader can judge what they describe, and that the rounding discipline applies to adjustments, rates, and the final opinion as well.
Real-World Application
Analyzing forty-one sales in a subdivision, an appraiser computes a mean of three hundred twenty-seven thousand four hundred eighty-three dollars and sixty-two cents and a median of three hundred nineteen thousand dollars, with two custom homes well above the rest of the range. The report presents the mean as approximately three hundred twenty-seven thousand five hundred dollars, presents the median alongside it, notes the two high sales as the reason the mean sits above the median, and states the sample size, the twelve-month period, and the subdivision boundaries the data covers.
More Statistics Questions
A set of comparable sales has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation?
A property sold for $400,000 and resold three years later for $463,050 with no physical change. What compound annual rate does this indicate?
A histogram of neighborhood sale prices shows two distinct peaks. What does this most likely mean?
What does it mean to validate a regression model?
In a market study, what does a frequency distribution of sale prices show?
An appraiser includes months elapsed since each sale as a variable in a price model. What is this intended to capture?
An appraiser presents a statistical analysis in a report. What must accompany it for the reader to weigh it?
An R-squared of 0.86 in a sales model indicates that:
Which measure would best summarize the most common lot size in a subdivision?
Paired sales analysis and regression differ mainly in that regression:
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