A sample that systematically excludes part of the population produces:
Correct Answer
D) Biased results regardless of sample size
Why this is correct: The correct answer is "Biased results regardless of sample size." Bias is a systematic error in the sampling method that excludes a segment of the population. This error is directional and does not diminish by simply increasing the sample size; a larger sample of a systematically flawed group will still produce a biased estimate. The original explanation correctly notes that bias is a direction, not a magnitude, and more observations of the wrong population do not correct the fundamental flaw. Why the other choices are wrong: "Results identical to a census" is wrong because a census includes the entire population, while this sample excludes part of it, so the results will differ. "More precise estimates than a random sample" is wrong because systematic exclusion introduces bias, which reduces accuracy; a properly drawn random sample is generally more reliable. "Errors that shrink as the sample grows" is wrong because the systematic error (bias) persists regardless of sample size; increasing the sample only reduces random sampling error, not bias. Exam tip: Remember the key distinction: increasing sample size reduces random error, but it cannot fix a biased sampling method.
Why This Is the Correct Answer
Systematic exclusion produces biased results regardless of sample size, because bias is a property of the selection method rather than of the quantity selected. Adding observations from the same flawed frame reproduces the same distortion at greater volume. The dangerous consequence is that the estimate looks more reliable as the sample grows, since random error shrinks while the systematic error sits untouched. Only changing how the data is gathered can correct it.
Why the Other Options Are Wrong
Option A: Results identical to a census
A census covers the entire population, which is exactly what a systematically incomplete sample does not do. If the two agreed, the exclusion would not have been systematic in the first place. The option describes the absence of the very problem the stem posits.
Option B: More precise estimates than a random sample
Precision and accuracy are different qualities: a biased sample can be highly precise, producing tightly clustered estimates that cluster around the wrong value. Precision without accuracy is arguably worse than neither, because it invites unwarranted confidence. A properly drawn random sample may be less precise but is unbiased.
Option C: Errors that shrink as the sample grows
Shrinking with sample size is the defining behavior of random error, not bias, and confusing the two is the exact error the item targets. More observations tighten the interval around whatever the biased sample converges to. The distortion persists at any size.
Bias Is a Direction, Not a Size
Random error is noise that averages out. Bias is a thumb on the scale that never lifts. Adding data quiets the noise and leaves the thumb exactly where it was.
How to use: When a stem describes a systematic exclusion, choose the answer saying bias persists regardless of size. Reserve answers about shrinking error for stems describing ordinary sampling variation.
Exam Tip
Ask what the data source cannot see. In residential work the classic blind spots are for-sale-by-owner sales and builder transactions that never appear in the MLS.
Common Mistakes to Avoid
- -Trying to fix a coverage gap by enlarging the sample
- -Treating MLS data as the complete universe of transactions
- -Mistaking tight clustering for accuracy
Concept Deep Dive
Analysis
Statistical error comes in two kinds that behave completely differently. Random error, sometimes called sampling error, is the ordinary variation that arises because a sample is not the whole population; it scatters in both directions around the truth and shrinks predictably as the sample grows, roughly with the square root of sample size. Bias is systematic error, a consistent pull in one direction caused by how the data was gathered rather than by how much of it was gathered. Collecting more observations from a systematically incomplete frame simply produces a larger, more confidently stated wrong answer, because every additional observation carries the same distortion. In appraisal this matters concretely: pulling only MLS sales in a market where a third of transactions are for-sale-by-owner or builder direct, pulling only closed sales during a rapidly changing market while ignoring pendings, or pulling only lender-required appraisals all produce samples that exclude part of the relevant population. The cure is fixing the sampling frame, never enlarging it.
Background Knowledge
You need the distinction between random sampling error and systematic bias, and the concept of a sampling frame and how coverage gaps arise. You should also know the common data-source gaps in appraisal practice, including for-sale-by-owner transactions, builder sales, off-market and pocket listings, and portfolio or entity transfers.
Real-World Application
An appraiser deriving a market conditions rate from MLS data alone learns that a builder sold sixty homes directly in the subject's subdivision, none of them listed. She supplements with recorded deed data to capture those transactions, recomputes the trend, and documents both the gap and the correction.
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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