An area’s median sale price falls 6% while median price per square foot rises 2%. Which is a plausible explanation requiring further investigation?
Correct Answer
C) The mix of homes sold may have shifted, for example toward smaller homes
A changing mix of sold properties, including a higher share of smaller homes, can help explain falling median total price alongside rising median unit price. These two summaries do not uniquely identify that cause or prove uniform price movement, a calculation error or an appropriate time-adjustment sign. Investigate composition, dates and comparable market evidence before attribution.
Why This Is the Correct Answer
Option C is correct because a shift in the mix of homes sold, such as a higher share of smaller homes, can explain a lower median total price alongside a higher median unit price. These summaries do not prove that cause by themselves, so the appraiser should investigate composition, sale dates and comparable market evidence before drawing a conclusion.
Why the Other Options Are Wrong
Option A: At least one of the two summary figures must be arithmetically wrong
Option A says at least one figure must be arithmetically wrong, but the two figures can both be correct when the mix of sold homes changes. The divergence calls for investigation, not an assumption of error.
Option B: Each property in the area has declined in value by 6 percent
Option B says each property declined 6 percent, but a change in a median does not show uniform movement for every property. The rising price per square foot also argues against reading the 6 percent drop as a uniform decline.
Option D: Each comparable sale now requires a negative time adjustment
Option D says each comparable now needs a negative time adjustment, but these summaries do not establish the direction of a time adjustment. A specific time adjustment may differ from the overall trend and must be supported by market evidence.
Mix moves medians
When total price and unit price disagree, first ask what kinds of homes sold. A change in mix can move a median without any change in value.
How to use: Use this when two market indicators point in opposite directions.
Exam Tip
When a question asks for a plausible explanation to investigate, favor answers that call for analysis over answers stating that something must be true.
Common Mistakes to Avoid
- -Assuming a calculation error when indicators diverge
- -Treating a median change as a uniform change for every property
- -Setting a time adjustment from summary medians alone
Concept Deep Dive
Analysis
This question tests interpreting conflicting summary statistics. A falling median price with a rising median price per square foot can happen when the homes that sold are smaller on average, since smaller homes tend to sell for less in total but often more per square foot. The candidate should pick the explanation that is plausible and calls for further investigation rather than one that jumps to a conclusion.
Background Knowledge
Median price and median price per square foot can move in different directions when the composition of sales changes, because unit prices often vary with size. Summary statistics describe the sales that happened to occur, not necessarily a change in value for a constant-quality property. Appraisers investigate composition before attributing movement to market change.
Real-World Application
An appraiser sees the area's median sale price drop while median price per square foot climbs. Checking the data, she finds that a new condo-style development of small units dominated recent sales. She reports the composition shift rather than concluding values fell.
More Statistics Questions
Sale prices are $270,000, $290,000, $300,000, $310,000, $330,000. Treat the listed observations as the complete population and divide by n when computing the standard deviation. Report to the nearest dollar.
A sales sampling frame systematically excludes a relevant part of the target market. What is the principal risk?
An appraiser estimates a market-wide price trend using only sales data from one brokerage that specializes in luxury homes, without checking how other segments are represented. What is the principal concern?
Compared with analyzing one matched sale pair for one feature, what can a suitably specified multiple regression do?
The base-period median sale price is $400,000 and the current-period median is $460,000. Compute the price relative defined as current ÷ base, as a decimal to three places.
The assessment-to-sale ratios are 0.8, 0.85, 0.9, 0.92, 0.95, 0.98, 1.02, 1.05, 1.08, 1.1, 1.15, 1.2. Calculate COD as [average absolute deviation from the median ÷ median]×100. For even n, average the two middle ratios. Report the COD as a percentage to two decimals.
Assessment-to-sale ratios are 0.94, 0.96, 0.98, 1, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Market data show a first quartile sale price of $405,000 and a third quartile sale price of $495,000. What is the interquartile range, to the nearest dollar?
Assessment-to-sale ratios are 0.96, 0.98, 0.99, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
Given first quartile $400,000, median $440,000 and third quartile $500,000, compute the trimean (Q1+2×median+Q3)/4. Report to the nearest dollar.
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Previous Question
Sale-price mean is $480,000, median $420,000 and standard deviation $90,000. Calculate Pearson's second skewness coefficient 3(mean − median) / standard deviation, to two decimals.
Next Question
Sale prices are $190,000, $210,000, $230,000, $250,000, $270,000, $300,000, $360,000. Using the median of each half excluding the overall median, Q1=$210,000 and Q3=$300,000. Compute the interquartile range Q3−Q1, to the nearest dollar.