Sale-price observations are $185,000, $192,000, $188,000, $195,000, $190,000. Compute the median; order the observations first and average the two middle values if n is even. Report to the nearest dollar.
Correct Answer
A) $190,000
Ordered values: $185,000, $188,000, $190,000, $192,000, $195,000. The middle observation is 190000. Common errors: reporting the lowest observation gives $185,000; reporting the highest observation gives $195,000; taking the middle value of the unordered list gives $188,000.
Why This Is the Correct Answer
Option A is correct because ordering the prices gives $185,000, $188,000, $190,000, $192,000, $195,000. With five observations, the middle (third) value is $190,000. Two observations lie below it and two lie above it.
Why the Other Options Are Wrong
Option B: $185,000
Option B, $185,000, simply reports the lowest observation. The median is the third ordered value, $190,000.
Option C: $195,000
Option C, $195,000, simply reports the highest observation. The median is the third ordered value, $190,000.
Option D: $188,000
Option D, $188,000, is the middle (third) value of the list as originally written, before sorting. Once the prices are ordered, the third value is $190,000.
Sort first, then split
Before you split the data in half to find the median, sort it; splitting an unsorted list gives a random value.
How to use: Use this two-step reminder on every median calculation question.
Exam Tip
If one option equals the middle value of the list exactly as printed, check whether the list was sorted. Exam writers often use the unsorted middle as a distractor.
Common Mistakes to Avoid
- -Taking the middle value of the unsorted list
- -Reporting the lowest or highest value as the median
- -Confusing the median with the mean
Concept Deep Dive
Analysis
This question tests whether the candidate orders the data before finding the median. The prices are listed out of order, so the third value as listed is not the median. After sorting, the third of five values is the answer.
Background Knowledge
The median is defined on ordered data: it is the point with half the observations below and half above. Data collected from sales records are rarely in order, so sorting is the essential first step. For an odd count, the median is the single middle observation.
Real-World Application
An appraiser pulls five comparable sales from a records search sorted by closing date. Before reporting the median price, he re-sorts them by price and finds the median is $190,000, not the $188,000 that sat in the middle of the date-sorted list.
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Sale-price observations are $250,000, $260,000, $255,000, $270,000, $255,000. Compute the median; order the observations first and average the two middle values if n is even. Report to the nearest dollar.
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For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.