Numerical adjusted indications are $288,000, $296,000, $303,000 and $316,000. What is their full numerical range? This does not independently justify retaining every observation.
Correct Answer
B) $288,000 to $316,000
minimum(288000,296000,303000,316000)=288000; maximum=316000. Common errors: reporting only the two middle indications gives $296,000 to $303,000; reporting the mean instead of the range gives $300,750 only; reporting the median instead of the range gives $299,500 only.
Why This Is the Correct Answer
Option B is correct because the smallest indication is $288,000 and the largest is $316,000, so the full numerical range is $288,000 to $316,000. Range is defined by the largest value and the smallest value in the data set.
Why the Other Options Are Wrong
Option A: $296,000 to $303,000
Option A is wrong because $296,000 to $303,000 reports only the two middle indications. The full range includes the lowest value, $288,000, and the highest, $316,000.
Option C: A single value of $300,750
Option C is wrong because a single value of $300,750 is the mean: ($288,000 + $296,000 + $303,000 + $316,000) ÷ 4 = $300,750. The question asks for the range, which is $288,000 to $316,000.
Option D: A single value of $299,500
Option D is wrong because a single value of $299,500 is the median: ($296,000 + $303,000) ÷ 2 = $299,500. The range is the span from $288,000 to $316,000, not one middle value.
Range Means Ends
Range is about the ends: lowest to highest, nothing in the middle.
How to use: Use this phrase to reject choices that show a middle value, mean or median.
Exam Tip
Sort the numbers from low to high first; the range is the first and last values.
Common Mistakes to Avoid
- -Reporting only the middle values as the range
- -Confusing the range with the mean
- -Confusing the range with the median
Concept Deep Dive
Analysis
This question tests the definition of range in a set of adjusted indications. The range runs from the smallest value to the largest value. The candidate must not confuse the range with the middle values, the mean or the median.
Background Knowledge
Range is a measure of spread, defined as the maximum value minus the minimum value, and it can also be stated as the low and high end points. Mean and median are measures of central tendency. Reporting the range does not by itself decide which indications deserve the most weight in reconciliation.
Real-World Application
After adjusting four comparables, an appraiser lists indications from $288,000 to $316,000. She reports that range in the reconciliation. She then explains which sales get the most weight and why.
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