For estimating a market-wide average, what is the principal limitation of using only four sales from a market with 200 annual transactions?
Correct Answer
D) Limited information; uncertainty and representativeness require assessment
Four observations provide limited information for broad population inference. Their relevance, variation and selection method also matter; the fraction four out of 200 alone does not determine adequacy for an appraisal assignment. Random-sampling confidence formulas do not automatically apply to a purposively chosen comparable set. Neither universal sufficiency nor an automatic prohibition follows from the count.
Why This Is the Correct Answer
Option D is correct because four observations provide limited information for broad population inference, so the resulting uncertainty and whether the sales represent the market must be assessed. Adequacy depends on the variation in the data, the relevance of the sales and how they were chosen, not on the count alone. Statistical reliability generally improves as the number of observations increases.
Why the Other Options Are Wrong
Option A: The sample is invalid for appraisal purposes because it is under 30 sales
Option A says the sample is invalid for appraisal purposes because it is under 30 sales. There is no universal 30-sale rule that disqualifies a sample; adequacy requires judgment about variation, relevance and the assignment.
Option B: Four sales are sufficient for population conclusions in this market
Option B says four sales are sufficient for population conclusions in this market. Four sales offer limited information about a 200-sale market, and sufficiency cannot be assumed without assessing uncertainty and representativeness.
Option C: Four observations are too many to analyze efficiently
Option C says four observations are too many to analyze efficiently. Four is a very small data set that is easy to analyze; the concern is too little information, not too much.
Few sales, more caution
The fewer the sales, the more caution and explanation the conclusion needs, but a small count is not an automatic ban.
How to use: Use this to reject answers that set rigid sample-size cutoffs in either direction.
Exam Tip
Be skeptical of answers that state a fixed minimum count as a universal rule. Prefer answers that call for assessing uncertainty and representativeness.
Common Mistakes to Avoid
- -Applying a fixed 30-sale minimum as a universal validity rule
- -Treating a tiny sample as enough for market-wide conclusions
- -Applying random-sampling formulas to a hand-picked set of comparables
Concept Deep Dive
Analysis
This question tests judgment about sample size and representativeness. Four sales provide limited information for drawing conclusions about a market of 200 annual transactions, but there is no fixed count that makes a sample automatically valid or invalid. The analyst must assess uncertainty, relevance, variation and how the sales were selected.
Background Knowledge
There is a general relationship between statistical reliability and the number of observations in a sample. Determining an adequate sample requires judgment, often including information about the actual variation in the data. Comparable sales are usually chosen purposively, so random-sampling confidence formulas do not automatically apply.
Real-World Application
An appraiser asked to describe average prices across a town with about 200 sales a year has only four verified sales from one subdivision. She reports the figure as limited evidence, explains its uncertainty and checks whether those sales resemble the wider market before generalizing.
More Statistics Questions
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Previous Question
The positive observations are $160,000, $250,000. Compute their simple geometric mean (product of all observations)^(1/n). Report to the nearest dollar.
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Ordered sale prices are $120,000, $160,000, $200,000, $280,000, $360,000, $440,000, $600,000, $720,000, $900,000. The first, second and third quartiles are taken as the 3rd, 5th and 7th observations, respectively. Skewness is measured as the distance from the median up to the third quartile minus the distance from the first quartile up to the median, divided by the interquartile range. What is this skewness measure, to two decimals?