Sale-price observations or stated extremes are $390,000, $410,000, $425,000, $440,000, $480,000. Compute the midrange (minimum+maximum)/2 to the nearest dollar.
Correct Answer
A) $435,000
(390000+480000)/2=435000. 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 $90,000; reporting the lowest observation gives $390,000; reporting the highest observation gives $480,000.
Why This Is the Correct Answer
Option A is correct because the minimum is $390,000 and the maximum is $480,000, so the midrange is ($390,000 + $480,000) / 2 = $870,000 / 2 = $435,000.
Why the Other Options Are Wrong
Option B: $90,000
Option B, $90,000, is the range, $480,000 - $390,000 = $90,000, a measure of spread rather than the midrange. The midrange is ($390,000 + $480,000) / 2 = $435,000.
Option C: $390,000
Option C, $390,000, simply reports the lowest observation instead of averaging the two extremes. The midrange is ($390,000 + $480,000) / 2 = $435,000.
Option D: $480,000
Option D, $480,000, simply reports the highest observation instead of averaging the two extremes. The midrange is ($390,000 + $480,000) / 2 = $435,000.
Midrange Is Halfway Between Extremes
The midrange sits exactly halfway between the lowest and highest values: add them and divide by two.
How to use: Use this phrase to keep the midrange separate from the range and the median.
Exam Tip
Watch for range-versus-midrange confusion: range subtracts the extremes, midrange averages them.
Common Mistakes to Avoid
- -Computing the range instead of the midrange
- -Confusing the midrange with the median
- -Reporting one extreme instead of averaging both
Concept Deep Dive
Analysis
This question tests the midrange, the average of the minimum and maximum values. Only the two extremes enter the calculation. The distractors come from computing the range or reporting one of the extremes.
Background Knowledge
The midrange is a measure of location that uses only the smallest and largest values, so it is highly sensitive to extremes. It differs from the median, the middle ordered value, and from the range, the largest value minus the smallest.
Real-World Application
An appraiser quickly summarizes five sales from $390,000 to $480,000 and notes a midrange of $435,000. Because the midrange depends only on the extremes, the appraiser also reports the median of $425,000 for a steadier picture.
More Statistics Questions
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