Days on market for recent sales are 15, 22, 28, 35 and 120. Which figure best describes typical marketing time?
Correct Answer
D) The median of 28 days across the five sales
Why this is correct: The median (28 days) is the middle value when data are ordered, unaffected by the outlier (120 days), so it best represents typical marketing time. Why the other choices are wrong: "The mean of 44 days across the five sales" is skewed by the outlier, overstating typical time. "The range of 105 days between the extremes" shows spread, not typical value. "The mode, since no value repeats in the set" is inapplicable; mode requires repeating values. Exam tip: Use median for typical value when data have outliers; mean is sensitive to extremes.
Why This Is the Correct Answer
The median of twenty-eight days is the better description because it is resistant to the single extreme observation and lands where four of the five sales actually are. Reporting it well means saying more than the number: state the measure used, note the range and the presence of the long marketing period, and consider whether that sale differed in price, condition, or exposure in a way that explains it. Marketing time also feeds directly into the exposure time opinion that accompanies a market value conclusion, so the appraiser should distinguish exposure time, which looks backward from the effective date, from marketing time, which looks forward. Where the outlier turns out to reflect a segment of the market the subject belongs to, the analysis changes and stratification may be warranted.
Why the Other Options Are Wrong
Option A: The mean of 44 days across the five sales
The mean of forty-four days exceeds four of the five observations, which is the tell that it has been pulled by the hundred and twenty day sale. Reporting it as typical would overstate marketing time for the segment and could distort both the exposure time opinion and the market conditions analysis. The mean is not wrong as a statistic; it is wrong as a description of typical here.
Option B: The range of 105 days between the extremes
The range measures dispersion, the distance between the smallest and largest observations, and it says nothing about where the center of the data lies. It is useful reported alongside a central measure, since it discloses the presence of the long sale. Offering a dispersion measure in answer to a question about typical value confuses the two families of statistic.
Option C: The mode, since no value repeats in the set
The mode is the most frequently occurring value and requires repetition to exist, which this set does not have, so there is no mode to report. The option even concedes that no value repeats, which makes it self-defeating. Mode is more useful for categorical data or for continuous data grouped into intervals.
One Long Sale Drags the Mean
Put the numbers on a line and drop the outlier on the far end. The mean slides toward it; the median stays put with the crowd. When your average is longer than most of your data, you are describing the outlier.
How to use: Order the data and look for an observation far from the cluster before choosing a statistic. With an outlier present, report the median and disclose the range and the extreme value rather than deleting it. Investigate what made the outlier different, since it may reveal a segment worth analyzing separately.
Exam Tip
Outlier in the data means median for typical. Report the range alongside it so the reader sees the spread.
Common Mistakes to Avoid
- -Reporting a mean that exceeds most of the observations in the data set
- -Deleting an outlier rather than investigating what made it different
- -Confusing exposure time, which looks backward from the effective date, with forward-looking marketing time
Concept Deep Dive
Analysis
This item tests the choice among measures of central tendency when a data set contains an extreme value. The mean adds every observation and divides, so each value pulls the result toward itself in proportion to its distance from the others, which makes a single extreme observation capable of moving the mean well away from the bulk of the data. The median takes the middle observation of the ordered set, so it depends on rank rather than magnitude and is largely unmoved by how extreme the extremes are. In the stem, four sales cluster between fifteen and thirty-five days and one sat for a hundred and twenty, and the mean of forty-four days is longer than four of the five actual observations, which is a clear signal that it is describing the outlier rather than the market. The median of twenty-eight sits inside the cluster and represents what a typical seller experienced. The right practice is not to discard the long sale, which may reveal something worth investigating, but to report the measure that describes typical behavior and to discuss the outlier separately.
Background Knowledge
You need to know the three measures of central tendency and their behavior, with the mean sensitive to extreme values, the median resistant and based on rank, and the mode requiring repetition. You should know the measures of dispersion, including range and standard deviation, and that dispersion and central tendency answer different questions. You also need to know the distinction between exposure time, which is the estimated length of time the property would have been on the market before the hypothetical sale at the effective date, and marketing time, which is a forward-looking estimate.
Real-World Application
Analyzing marketing time in a small subdivision, the appraiser finds four sales closing within fifteen to thirty-five days and one that lingered a hundred and twenty. Investigating, she learns the slow sale was initially listed forty percent above the eventual price. She reports a median of twenty-eight days as typical, discloses the range and the overpriced listing, and uses the cluster rather than the mean to support her exposure time opinion.
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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An appraiser presents a statistical analysis in a report. What must accompany it for the reader to weigh it?
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Paired sales analysis and regression differ mainly in that regression:
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