Four competitive cash-equivalent sales had days on market (DOM) of 12, 16, 20, and 28 days. What is the median DOM?
Correct Answer
B) 18 days
Ordered sample 12,16,20,28; median=(16+20)/2=18 days. Use the same population, period and price/listing definition throughout. Common errors: computing the mean instead of the median gives 19 days; taking only the lower middle value gives 16 days; averaging the two highest values gives 24 days.
Why This Is the Correct Answer
Option B is correct because the ordered DOM values are 12, 16, 20 and 28, and the median is the average of the two middle values: (16 + 20) / 2 = 18 days. Two observations fall below 18 and two above it.
Why the Other Options Are Wrong
Option A: 16 days
Option A is wrong because 16 days takes only the lower middle value. With an even count, the median averages both middle values: (16 + 20) / 2 = 18 days.
Option C: 19 days
Option C is wrong because 19 days is the mean, not the median: (12 + 16 + 20 + 28) / 4 = 76 / 4 = 19. The median is (16 + 20) / 2 = 18 days.
Option D: 24 days
Option D is wrong because 24 days averages the two highest values: (20 + 28) / 2 = 24, the median of the upper half only. The median of all four values averages the two middle ones: (16 + 20) / 2 = 18 days.
Even count, average middles
With an even count there is no single middle, so average the two in the center.
How to use: Use this whenever a median question has an even number of values.
Exam Tip
Count the observations first; if the count is even, expect distractors that pick one middle value or compute the mean.
Common Mistakes to Avoid
- -Choosing one of the two middle values instead of averaging them
- -Reporting the mean as the median
- -Averaging the wrong pair of values
- -Forgetting to order the data first
Concept Deep Dive
Analysis
This question tests finding the median for an even number of observations. With four ordered values, the median is the average of the two middle values, not either one alone and not the mean.
Background Knowledge
For an odd number of observations the median is the single middle value, and for an even number it is the average of the two middle values. Median days on market is a common market conditions indicator because it is less affected by unusually long or short marketing periods. The same population and period should be used throughout.
Real-World Application
An appraiser has four competing cash-equivalent sales with marketing times of 12, 16, 20 and 28 days. Reporting a median DOM of 18 days gives a typical marketing time that is not pulled upward by the 28-day sale.
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