Three approach indications are $398,000, $412,000 and $438,000. What is their numerical range (highest minus lowest)?
Correct Answer
C) $40,000
The maximum is $438,000 and the minimum is $398,000. Their difference is $40,000. Adjacent gaps and the arithmetic mean do not measure the full range. The range is a descriptive statistic, not the reconciled value opinion.
Why This Is the Correct Answer
Option C is correct because the highest indication is $438,000 and the lowest is $398,000, and $438,000 − $398,000 = $40,000. The range is defined as the largest value minus the smallest value in a data set.
Why the Other Options Are Wrong
Option A: $14,000
Option A, $14,000, is the gap between the two lowest indications ($412,000 − $398,000 = $14,000). That is an adjacent gap, not the full range; the range is $438,000 − $398,000 = $40,000.
Option B: $26,000
Option B, $26,000, is the gap between the two highest indications ($438,000 − $412,000 = $26,000). It omits the lowest indication; the full range is $438,000 − $398,000 = $40,000.
Option D: $416,000
Option D, $416,000, is the arithmetic mean of the indications: ($398,000 + $412,000 + $438,000) ÷ 3 = $1,248,000 ÷ 3 = $416,000. The mean measures central tendency, not spread; the range is $40,000.
Range is top minus bottom
To find the range, subtract the lowest number from the highest number and ignore the ones in between.
How to use: Use this whenever a question asks for the range of a set of indications.
Exam Tip
Identify the highest and lowest values first. Answers that equal an adjacent gap or the average are distractors.
Common Mistakes to Avoid
- -Subtracting adjacent values instead of highest minus lowest
- -Confusing the range with the average
- -Treating the range as the reconciled value
Concept Deep Dive
Analysis
This question tests the definition of the range of a set of indications. The range is the highest value minus the lowest value. It describes the spread of the indications and is not itself a value conclusion.
Background Knowledge
The range is a simple measure of dispersion. In reconciliation, a wide range among approach indications signals the need to examine the support for each one, but the range itself does not determine the final value.
Real-World Application
An appraiser notes that the three approaches span $40,000 on a modest home. Because the spread is meaningful relative to value, the appraiser reviews the cost approach depreciation and the income approach rent data before reconciling.
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Previous Question
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