Nine sales cluster between $240,000 and $260,000, but one estate sale closed at $95,000. Which measure of central tendency best describes this market?
Correct Answer
D) The median, since one extreme cannot skew it
Why this is correct: The original explanation notes that a single extreme value (the $95,000 estate sale) pulls the mean down, while the median, being the middle value in an ordered list, is unaffected by outliers. With nine sales clustered between $240k-$260k, the median will lie within that cluster, representing the typical transaction. Why the other choices are wrong: The mean, since it uses every observation would be skewed downward by the outlier, misrepresenting the typical price. The range, since it shows both extremes describes spread, not central tendency. The mode, since prices repeat frequently might work if there is a frequent repeating price, but the median is explicitly robust against the single extreme. Exam tip: When data has a significant outlier, the median is usually the better measure of central tendency.
Why This Is the Correct Answer
The median takes the middle ranked value, so a single extreme observation shifts it by one ranking position and the result stays within the cluster where the market actually is.
Why the Other Options Are Wrong
Option A: The mean, since it uses every observation
Using every observation is precisely the mean's weakness here, since the outlier drags the average well below the cluster.
Option B: The range, since it shows both extremes
The range reports the extremes rather than the centre, and is not a measure of central tendency at all.
Option C: The mode, since prices repeat frequently
The mode requires repeated values. Sale prices rarely repeat exactly, making it uninformative for this data.
One Weird Sale Cannot Move the Middle
One Weird Sale Cannot Move the Middle. It shifts the ranking by one place and that is all.
How to use: Scan for outliers before choosing a measure. Their presence is what decides between mean and median.
Exam Tip
Investigate the outlier as well as excluding it from the average. An estate sale at that discount probably fails verification.
Common Mistakes to Avoid
- -Reporting a mean without checking for outliers
- -Treating the range as a measure of central tendency
- -Tolerating an outlier rather than investigating it
Concept Deep Dive
Analysis
The three measures of central tendency behave differently in the presence of an outlier, and this data set is designed to show it. The mean adds every observation and divides, so the $95,000 estate sale pulls the average down by roughly $16,000 from where the bulk of the market actually sits — producing a figure no property in the data set is near. The median ranks the values and takes the middle one, so a single extreme observation moves the ranking position by one place and nothing more; the result stays inside the $240,000 to $260,000 cluster where the market genuinely is. That resistance to extreme values is exactly why the median is the standard measure for housing prices, whose distributions are routinely skewed. The estate sale itself deserves separate attention: a price that far below the cluster suggests a non-arm's-length or distressed transaction, which likely fails the verification test and should be excluded from the analysis on that ground rather than merely tolerated.
Background Knowledge
Central tendency measures include the mean, median and mode. The median is resistant to outliers, making it the standard measure for skewed distributions such as housing prices.
Real-World Application
An appraiser reports a $248,000 median rather than a $232,000 mean, and separately notes the estate sale as a non-arm's-length transaction excluded from the analysis.
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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