An appraiser is analyzing three competitive vacant land sales that closed at $215,000, $220,000, and $230,000 after cash-equivalent adjustment. What is the median land value indication?
Correct Answer
B) $220,000
Ordered prices = $215,000, $220,000, $230,000; middle observation = $220,000. The indicated value is $220,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: computing the mean instead of the median gives $221,667; reporting the lowest sale gives $215,000; reporting the highest sale gives $230,000.
Why This Is the Correct Answer
Option B is correct because the median of an odd number of items is the middle item when arranged by size. Ordered, the sales are $215,000, $220,000 and $230,000, so the median is $220,000.
Why the Other Options Are Wrong
Option A: $215,000
Option A, $215,000, is the lowest of the three sales, not the middle observation. The median of $215,000, $220,000 and $230,000 is $220,000.
Option C: $221,667
Option C, $221,667, is the mean rather than the median: ($215,000 + $220,000 + $230,000) ÷ 3 = $221,667. The median is the middle value, $220,000.
Option D: $230,000
Option D, $230,000, is the highest of the three sales, not the middle observation. The median is $220,000.
Median sits in the middle
Median, like the median strip of a highway, is in the middle. Line the numbers up and take the center one.
How to use: Use this to avoid confusing the median with the mean.
Exam Tip
Sort the values first; then check whether the count is odd or even before picking the median.
Common Mistakes to Avoid
- -Calculating the mean when the median is asked for
- -Picking the middle value without sorting first
- -Using unadjusted or non-competitive sales in the array
Concept Deep Dive
Analysis
This question tests the median as a measure of central tendency. Arrange the adjusted sales in order and pick the middle value for an odd number of observations. Distinguish the median from the mean and from the extremes.
Background Knowledge
The median is the middle value in an ordered odd-numbered set, or the average of the two central values in an even-numbered set. It is less affected by extreme values than the mean. The sales should be competitive and adjusted as needed before any statistic is used.
Real-World Application
An appraiser has three verified, cash-equivalent sales of competing building lots after adjustment. She reports the median as one indication and reconciles it with her analysis of which sale is most comparable.
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