Five recent closed sales in the subject's market area show days on market (DOM) of 15, 40, 21, 28, and 24. What is the median DOM?
Correct Answer
B) 24 days
Ordered days = 15, 21, 24, 28, 40; middle observation = 24 days. Keep the stated numerator, denominator and units distinct. Common errors: computing the mean instead of the median gives 26 days; taking the middle value of the unordered list gives 21 days; reporting the longest DOM gives 40 days.
Why This Is the Correct Answer
Option B is correct because ordering the days on market gives 15, 21, 24, 28, 40, and the middle (third) observation is 24 days. The median is the middle value of the ordered sample, so the median DOM is 24 days.
Why the Other Options Are Wrong
Option A: 21 days
Option A is wrong because 21 days is the middle value of the unordered list (15, 40, 21, 28, 24). The values must be ordered first: 15, 21, 24, 28, 40, giving a median of 24 days.
Option C: 26 days
Option C is wrong because 26 days comes from computing the mean instead of the median ((15 + 40 + 21 + 28 + 24) / 5 = 128 / 5 = 25.6, about 26). The median is the middle ordered value, 24 days.
Option D: 40 days
Option D is wrong because 40 days is the longest DOM in the sample, not the middle value. Ordering the values gives 15, 21, 24, 28, 40, so the median is 24 days.
Median sits in the middle
Like the median strip down the middle of a highway, the median is the value in the middle, but only after you line the numbers up in order.
How to use: Use the highway median image to remember to sort first, then pick the middle.
Exam Tip
Sort the values before finding the median. With an odd count, the median is the single middle value; do not average all values.
Common Mistakes to Avoid
- -Picking the middle value without sorting
- -Calculating the mean instead of the median
- -Reporting the maximum value as typical
Concept Deep Dive
Analysis
This question tests calculation of a median. The values must be put in order before choosing the middle observation. With five values, the third ordered value is the median.
Background Knowledge
The median is the middle value in an ordered data set and is less affected by unusually high or low values than the mean. Market conditions reporting commonly uses median days on market and median sale prices for this reason.
Real-World Application
An appraiser reviewing five recent comparable sales lists their days on market and sorts them to find a median of 24 days. The appraiser reports this median as a typical marketing time indicator for the segment.
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