Three approach indications are $401,000, $412,000 and $438,000. What is their median as a numerical summary?
Correct Answer
D) $412,000
With three ordered observations, the median is the middle one: $412,000. The minimum, maximum and arithmetic mean are different statistics. Computing the median does not establish that the appraiser should report it as the final reconciled market value.
Why This Is the Correct Answer
Option D is correct because the median of an odd number of ordered items is the middle item. Ordered, the values are $401,000 < $412,000 < $438,000, so the middle observation is $412,000. Computing a median is a numerical summary and does not by itself make that figure the reconciled market value.
Why the Other Options Are Wrong
Option A: $401,000
Option A is wrong because $401,000 is the minimum, the lowest of the three ordered values, not the middle one. The median is the second of the three, $412,000.
Option B: $438,000
Option B is wrong because $438,000 is the maximum, the highest of the three ordered values, not the middle one. The median is $412,000.
Option C: $417,000
Option C is wrong because $417,000 is the arithmetic mean, not the median: ($401,000 + $412,000 + $438,000) / 3 = $1,251,000 / 3 = $417,000. The median is the middle ordered value, $412,000.
Median sits in the middle
Like the median strip down the middle of a highway, the median is the value in the middle once the data are lined up in order.
How to use: Use this to separate the median from the mean, minimum and maximum on statistics questions.
Exam Tip
Always put the values in order before picking the median. Distractors often include the mean, so compute it to recognize it.
Common Mistakes to Avoid
- -Calculating the mean when the median is asked for
- -Choosing the middle value without first ordering the data
- -Treating the median of indications as the final reconciled value
Concept Deep Dive
Analysis
This question tests the definition of the median. With an odd number of observations arranged by size, the median is the middle item. Arrange $401,000, $412,000 and $438,000 in order and pick the second one; do not confuse it with the minimum, maximum or mean.
Background Knowledge
The median divides an ordered data set into two equal halves. For an odd count it is the middle value; for an even count it is the average of the two central values. The mean adds all values and divides by the count, so it is pulled toward extreme values more than the median.
Real-World Application
An appraiser summarizes three approach indications in a table and notes the median as a descriptive statistic. The appraiser then reconciles based on reliability and explains that the final opinion is not simply the median.
More Reconciliation Questions
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An otherwise applicable valuation approach cannot be developed reliably from the available data. The remaining scope can produce credible assignment results. What should the appraiser do?
May an appraiser use a hypothetical condition in any assignment?
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An appraiser proposes to assume there are no hidden defects. Which fact would characterize that assumption as extraordinary under the USPAP 2024 definition, rather than justify dismissing it as routine boilerplate?
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