Nine sale prices have median $412,000 and mean $468,000. Which is a plausible distributional explanation, without inferring a time trend from these summaries alone?
Correct Answer
B) Relatively high prices in the upper tail can pull the mean upward
A high-value upper tail can pull the mean above the median. The two summary numbers alone do not establish that specific observations are erroneous outliers or that the market rose or fell; dates and the full distribution would be needed. They also do not prove a median arithmetic error or make nine observations unanalyzable.
Why This Is the Correct Answer
Option B is correct because relatively high prices in the upper tail can pull the mean above the median, which fits a mean of $468,000 and a median of $412,000. When the right tail is heavier than the left, the mean tends to exceed the median. Dates and the full distribution would be needed to say more.
Why the Other Options Are Wrong
Option A: The median must contain an arithmetic error
Option A says the median must contain an arithmetic error. A median below the mean is a normal result in a right-skewed data set and does not by itself indicate any error.
Option C: Nine observations cannot be described statistically
Option C claims nine observations cannot be described statistically. Nine values can be summarized with a median and mean, though conclusions from a small sample should be drawn with care.
Option D: The market must have declined, pulling the median below the mean
Option D says the market must have declined, pulling the median below the mean. The median and mean contain no information about sale dates, so they cannot show a market trend in either direction.
Mean follows the tail
The mean is pulled toward the longer tail, so a mean above the median points to a heavier high-price tail.
How to use: Use this to interpret any question comparing a mean with a median.
Exam Tip
Choose the distributional explanation; answers that infer market direction or errors from summary figures alone overreach.
Common Mistakes to Avoid
- -Reading a market trend into a gap between mean and median
- -Assuming the median is wrong because it differs from the mean
- -Believing small samples cannot be summarized at all
Concept Deep Dive
Analysis
This question tests interpreting a mean that exceeds the median. A mean of $468,000 above a median of $412,000 suggests a heavier upper tail, where some relatively high prices pull the mean up. Summary figures alone do not show a time trend, an arithmetic error or that the sample is too small.
Background Knowledge
In a symmetric distribution the mean and median are close. In a right-skewed distribution, high values pull the mean above the median; in a left-skewed one, the mean falls below. Detecting a market trend requires analyzing prices over time, not comparing two summary statistics.
Real-World Application
An appraiser sees that nine recent sales have a median of $412,000 but a mean of $468,000. Reviewing the list, the appraiser finds two lakefront homes near $650,000 pulling the average up, and relies more on the median when describing typical prices.
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.
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
The assessment-to-sale ratios are 0.9, 0.95, 1.05, 1.1. 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.
Next Question
Sale-price observations are $290,000, $310,000, $325,000, $340,000, $385,000. Compute the arithmetic mean. Report to the nearest dollar.