A trend line fitted to quarterly median prices is used to adjust older sales. What must be confirmed first?
Correct Answer
A) That the medians rest on adequate sale counts
Why this is correct: A median price can be skewed by a small number of sales in a quarter, reflecting a change in the mix of properties sold rather than a true market trend. Before using a trend line from median prices, you must verify that each quarterly median is based on a sufficient number of sales to be reliable. Why the other choices are wrong: "That every quarter contains the same properties" is impossible and unnecessary. "That the trend line passes through every point" is not required; trend lines often approximate. "That the trend will continue into future quarters" is about forecasting, not confirming historical data reliability. Exam tip: Statistical reliability first: check sample size before using data for adjustments.
Why This Is the Correct Answer
Option A is correct because a median resting on too few sales is unreliable, and a trend line is only as good as the points it connects. Adequate counts per quarter make each median a stable estimate of central tendency rather than an artifact of which properties happened to close. This check should precede any use of the line for market conditions adjustments, and it pairs naturally with stratifying the data or shifting to price per square foot to control for mix. Where counts are thin, combining quarters into half-year periods is a common remedy.
Why the Other Options Are Wrong
Option B: That every quarter contains the same properties
Requiring identical properties in every quarter is impossible, since different homes sell in each period; that is the nature of transaction data. The concern about mix is real, but it is managed through stratification, adequate sample sizes, or a repeat-sales or price-per-square-foot approach, not by demanding the same properties. Setting an unattainable condition would rule out time-series analysis entirely.
Option C: That the trend line passes through every point
A trend line is deliberately not required to pass through every point, because it summarizes the central tendency across observations and the residuals are informative. A line touching every point would be interpolation rather than a trend and would fit noise as though it were signal. Perfect fit in a real data set is a warning of overfitting, not a sign of quality.
Option D: That the trend will continue into future quarters
Nothing about a fitted trend guarantees continuation, and the appraiser is using it to adjust past sales to the effective date rather than to forecast forward. Extending a trend into future quarters would be extrapolation and would require separate support. The question concerns retrospective adjustment, where past reliability is the relevant issue.
Check the points before the line
A trend line is only as trustworthy as the dots it connects. Ask how many sales stand behind each dot before you believe the slope.
How to use: On any question about a statistical tool, look for the answer that verifies the input data. Options demanding perfect fit or guaranteed continuation misunderstand what a trend line is.
Exam Tip
Distinguish adjusting old sales to today, which is interpolation within observed data, from projecting forward, which is extrapolation. Only the first is what a market conditions adjustment does.
Common Mistakes to Avoid
- -Fitting a trend to periods with too few sales
- -Attributing a mix shift to a market movement
- -Extending a fitted trend into future periods without support
- -Using raw median price where property size varies widely across periods
Concept Deep Dive
Analysis
This tests the reliability of the underlying data before any statistical technique is applied to it. A quarterly median price summarizes whatever sold in that quarter, so it reflects both price movement and the mix of properties that happened to transact. In a thin quarter with only a handful of sales, a couple of large or small homes can swing the median dramatically, and a trend line fitted through such points will track sampling noise and mix shifts rather than the market. Since the trend line is then used to adjust older comparables for market conditions, the error propagates directly into the value conclusion. Confirming adequate sale counts per period is the first check, and stratifying by property type or price tier, or using price per square foot rather than raw median price, further reduces mix effects. The technique is sound; its inputs are what require verification.
Background Knowledge
You need to understand market conditions adjustments and the common ways they are derived, including matched pairs across time, repeat sales, resales of the same property, and trend analysis of periodic statistics. You should also know that median and mean summaries reflect the mix of what sold, that small samples produce unstable statistics, and that appraisers remain responsible for verifying the data behind any technique.
Real-World Application
Building a market conditions adjustment for a small submarket, you find several quarters with only four or five sales and medians that swing wildly. You combine quarters into half-year periods, switch to median price per square foot to control for mix, and refit the trend, then cross-check the indicated rate against two resales of the same properties.
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?
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