A sample of four sales drawn from a market with 200 annual transactions is:
Correct Answer
D) Small — conclusions carry wide uncertainty
Why this is correct: A sample of four sales from 200 transactions is small, leading to high statistical uncertainty. Appraisers often use small, purposive samples (selecting the most comparable sales), which is acceptable, but conclusions should reflect the limited data with a range or caution, not a precise point estimate. Why the other choices are wrong: "Invalid unless randomly selected" is incorrect; appraisal samples are purposive, not random. "Statistically sufficient for any conclusion" is false; a small sample lacks the power for definitive conclusions. "Too large to analyze efficiently" is wrong; four sales are manageable, not too large. Exam tip: Small sample = wide confidence interval. Always qualify conclusions from limited data.
Why This Is the Correct Answer
Four sales is a small sample, and conclusions drawn from it carry wide uncertainty. That framing is accurate about both the statistics and the practice: the appraiser can still reach a supportable conclusion, but should reconcile toward a range rather than asserting a precise figure. It also prompts the right professional responses, which are to seek additional data, to look for corroboration from another approach, and to avoid overstating precision in the report. Small purposive samples are the norm in appraisal, which is why the caution matters rather than the disqualification.
Why the Other Options Are Wrong
Option A: Invalid unless randomly selected
Random selection is required for statistical inference about a population, not for appraisal, where the appraiser deliberately chooses the most comparable sales. A random sample of four transactions from the whole county could easily include properties nothing like the subject and would be far less useful. Purposive selection is a feature of the method rather than a defect.
Option B: Statistically sufficient for any conclusion
Four observations cannot support any conclusion, and claiming sufficiency for any conclusion ignores the relationship between sample size and uncertainty. A small sample is workable for a reasoned value opinion but has no power for statistical claims such as a reliable regression coefficient. The word any is the disqualifier.
Option C: Too large to analyze efficiently
Four sales is a very manageable quantity, easily analyzed by hand and typical of residential grids, which usually present three to six comparables. Nothing about four observations creates an efficiency problem. The option appears to test whether the candidate is reading the numbers at all.
Few but Fitting
Appraisers trade quantity for relevance on purpose. Four sales next door beat forty across the county. Accept the small sample, but never dress it up with precision it cannot carry.
How to use: When a stem gives a small sample, choose the answer that acknowledges wide uncertainty without declaring the sample invalid. Reject options demanding randomness, claiming sufficiency for anything, or complaining about size in the wrong direction.
Exam Tip
Purposive sampling is legitimate for a value opinion but not for statistical inference. If a question involves regression coefficients or confidence intervals, small purposive samples become a genuine problem.
Common Mistakes to Avoid
- -Reporting a precise point value from a very small sample without qualification
- -Running a regression on a handful of observations and treating the coefficients as reliable
- -Broadening the search geographically to enlarge the sample at the cost of relevance
Concept Deep Dive
Analysis
Appraisal practice and inferential statistics use samples differently, and understanding the difference resolves this item. A statistician draws a random sample so that the sample's properties can be generalized to the population with quantifiable confidence, and precision improves as the square root of sample size. An appraiser draws a purposive sample, deliberately selecting the few most similar properties rather than a random cross-section, because relevance matters more than representativeness when the goal is to value one specific property. That purposive approach is entirely legitimate and is what the sales comparison approach has always done. What it cannot do is deliver statistical confidence: four observations out of 200 transactions support a range and a reasoned judgment, not a precise point estimate with a tight interval. The honest response is to recognize the limitation, look for a consistent pattern across the few sales available, and express the conclusion with appropriate humility rather than false precision.
Background Knowledge
You need the distinction between purposive and random sampling and why appraisal uses the former, plus the basic relationship between sample size, random error, and confidence. You should also know that reconciliation weighs indications by the quantity and quality of supporting evidence, and that a value opinion may be expressed as a range where the data supports only that.
Real-World Application
An appraiser in a thin submarket finds only four reasonably comparable sales in eighteen months. She uses all four, notes that the limited data supports a range rather than a precise point, corroborates with an income indication, and states in the report how the scarcity of data affected her confidence.
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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