Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Correct Answer
B) $75,000
500000−425000=75000. The range is a spread measure; the average or maximum alone does not answer the question.
Why This Is the Correct Answer
Option B is correct because the largest price is $500,000 and the smallest is $425,000. The range is $500,000 - $425,000 = $75,000. It measures the spread between the two extreme observations.
Why the Other Options Are Wrong
Option A: $458,000
Option A, $458,000, is the mean: the prices total $2,290,000, and $2,290,000 / 5 = $458,000. The range is the maximum minus the minimum, $500,000 - $425,000 = $75,000.
Option C: $500,000
Option C, $500,000, is only the maximum price. The range subtracts the minimum from it: $500,000 - $425,000 = $75,000.
Option D: $450,000
Option D, $450,000, is the median of the ordered prices ($425,000, $440,000, $450,000, $475,000, $500,000). The range is $500,000 - $425,000 = $75,000.
Top minus bottom
The range is simply the top value minus the bottom value.
How to use: Use this phrase to avoid confusing the range with the mean, median or maximum.
Exam Tip
Range answers are differences, so they are usually much smaller than the individual prices listed.
Common Mistakes to Avoid
- -Reporting the maximum instead of the range
- -Confusing the range with the mean or median
- -Subtracting values that are not the extremes
Concept Deep Dive
Analysis
This question tests the range, the simplest measure of spread. You identify the largest and smallest values and subtract. The distractors are the mean, the maximum and the median of the same data.
Background Knowledge
The range is the largest value minus the smallest value in a data set. It is easy to compute but uses only the two most extreme points, so it says nothing about how the values in between are distributed.
Real-World Application
An appraiser summarizing five comparable sales notes they range from $425,000 to $500,000, a spread of $75,000. That range frames the reconciliation discussion before adjustments narrow the indicated values.
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