Sale-price observations or stated extremes are $370,000, $510,000. Compute the midrange (minimum+maximum)/2 to the nearest dollar.
Correct Answer
D) $440,000
(370000+510000)/2=440000. The midrange uses the two extremes and is not the sample median or full range. Common errors: computing the range instead of the midrange gives $140,000; reporting the lowest observation gives $370,000; reporting the highest observation gives $510,000.
Why This Is the Correct Answer
Option D is correct because the midrange is (minimum + maximum) ÷ 2 = ($370,000 + $510,000) ÷ 2 = $880,000 ÷ 2 = $440,000. It sits halfway between the two extremes. It is not the sample median or the full range.
Why the Other Options Are Wrong
Option A: $140,000
Option A, $140,000, is the range rather than the midrange: $510,000 − $370,000 = $140,000. The midrange averages the extremes, ($370,000 + $510,000) ÷ 2 = $440,000.
Option B: $370,000
Option B, $370,000, simply reports the lowest observation. The midrange is halfway between the extremes, ($370,000 + $510,000) ÷ 2 = $440,000.
Option C: $510,000
Option C, $510,000, simply reports the highest observation. The midrange is halfway between the extremes, ($370,000 + $510,000) ÷ 2 = $440,000.
Midrange means middle of range
The midrange is the midpoint of the range: add the low and high and divide by two.
How to use: Use the word mid to remember that you average the extremes rather than subtract them.
Exam Tip
If an option equals the high minus the low, it is the range distractor. The midrange lies halfway between the two extremes.
Common Mistakes to Avoid
- -Computing the range instead of the midrange
- -Reporting one of the extremes as the center
- -Treating the midrange as the median
Concept Deep Dive
Analysis
This question tests the midrange, the average of the minimum and maximum values. With only two stated extremes, the calculation is a simple average of the two. Candidates must not confuse it with the range, which subtracts rather than averages.
Background Knowledge
The midrange is a quick measure of center based only on the two extreme values. Because it depends entirely on the extremes, it is highly sensitive to outliers. It is related to, but different from, the range, which measures spread.
Real-World Application
An appraiser briefly describing a neighborhood's price bracket of $370,000 to $510,000 notes a midrange of $440,000. She adds the median of the actual sales because the midrange depends only on the two extremes.
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