Recorded days on market for five recent closed sales are 15, 22, 28, 35 and 120. Which summary describes the sample center with less sensitivity to the unusually long listing?
Correct Answer
D) The median of 28 days across the five sales
The ordered middle observation is 28 days. Mean = (15+22+28+35+120)/5 = 44 days, influenced by the long listing. Range = 120−15 = 105 days describes spread. No value repeats, so there is no unique modal observation. The median summarizes this sample with less sensitivity to the high observation; it is not by itself a prospective marketing-time opinion.
Why This Is the Correct Answer
Option D is correct because the median of 15, 22, 28, 35 and 120 is the middle value, 28 days, and it does not move with the size of the 120-day listing. For data with extreme values in the tails, the median gives a better estimate of location than the mean. It describes this sample, not a forecast of marketing time.
Why the Other Options Are Wrong
Option A: The mean of 44 days across the five sales
Option A, the mean of 44 days, is (15 + 22 + 28 + 35 + 120) / 5 = 220 / 5 = 44. It is pulled upward by the 120-day listing, so it is more sensitive to that value, not less.
Option B: The range of 105 days between the extremes
Option B, the range of 105 days, is 120 − 15 = 105. It measures spread, not center, and it depends directly on the unusual listing.
Option C: The mode, since no value repeats in the set
Option C points to the mode while noting no value repeats in the set. With no repeated value there is no unique mode, so it cannot describe the center here.
Median ignores the loud one
One very large value shouts at the mean but barely whispers to the median, because the median only cares who is in the middle.
How to use: Use this to pick the median when a question highlights an unusual observation.
Exam Tip
When a question stresses an extreme value and asks for a resistant center, look for the median.
Common Mistakes to Avoid
- -Using the mean when the data contain an extreme value
- -Treating the range as a measure of center
- -Treating the median of past sales as a marketing-time opinion by itself
Concept Deep Dive
Analysis
This question tests choosing a measure of center that resists an extreme value. The days on market are 15, 22, 28, 35 and 120, and the 120-day listing pulls the mean up. The median, the middle ordered value of 28 days, is far less affected by that high observation.
Background Knowledge
The mean uses the size of each value, so one extreme observation can shift it substantially. The median depends only on the order of values, which makes it more resistant to outliers. When the right tail is heavier, the mean tends to sit above the median.
Real-World Application
An appraiser reporting market activity finds one sale that sat on the market for 120 days because of a pricing dispute. Reporting a median of 28 days, along with the range, gives readers a more typical picture than the 44-day mean.
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Previous Question
The assessment-to-sale ratios are 0.85, 0.9, 0.92, 0.95, 0.98, 1.02, 1.05, 1.08, 1.1, 1.15. 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.
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