Five sale prices are $200,000, $220,000, $230,000, $240,000 and $400,000. What are their mean and median, and which summary of this set is less sensitive to the high observation?
Correct Answer
A) Mean $258,000; median $230,000; prefer the median
Mean = 1,290,000 / 5 = $258,000; median is the third ordered observation, $230,000. For describing the center of these five prices with less sensitivity to the high observation, the median is the appropriate choice here. Neither summary alone establishes the subject property’s market value. The other options interchange or miscompute the summaries.
Why This Is the Correct Answer
Option A is correct because the mean is $1,290,000 / 5 = $258,000 and the median is the third ordered observation, $230,000. The median is less affected by extreme values than the mean, so it better describes the center of this set given the $400,000 sale. Neither summary by itself establishes a subject property's market value.
Why the Other Options Are Wrong
Option B: Mean $230,000; median $258,000; prefer the mean
Option B is wrong because it swaps the two summaries, listing a mean of $230,000 and a median of $258,000. The mean is $1,290,000 / 5 = $258,000 and the median is $230,000, and the mean is the more sensitive summary, so preferring it is also wrong.
Option C: Mean $258,000; median $240,000; prefer the mean
Option C is wrong because the median is not $240,000; that is the fourth ordered observation. The median of five ordered values is the third, $230,000, and the mean of $258,000 is more affected by the high sale, so the median, not the mean, should be preferred.
Option D: Mean $230,000; median $230,000; skew does not matter
Option D is wrong because the mean is not $230,000; ($200,000 + $220,000 + $230,000 + $240,000 + $400,000) / 5 = $258,000. The median is $230,000, and the skew from the $400,000 sale does matter because it pulls the mean upward.
Mean moves, median stays
An outlier drags the mean toward it, while the median stays at the middle of the ordered data.
How to use: Use this when a question asks which summary is less sensitive to an extreme value.
Exam Tip
Compute both statistics yourself before reading the options. Distractors often swap the mean and median or pick the wrong ordered position.
Common Mistakes to Avoid
- -Swapping the mean and the median
- -Picking the wrong position as the median
- -Preferring the mean when an outlier is present
Concept Deep Dive
Analysis
This question tests calculating the mean and median and recognizing which is less sensitive to an extreme value. The $400,000 sale is far above the others, pulling the mean up while leaving the median unchanged. Compute both, then identify the median as the more resistant summary.
Background Knowledge
The mean adds all values and divides by the count, so a single extreme value can shift it noticeably. The median is the middle ordered value and is less affected by extremes. When data are skewed, the median often gives a better picture of the typical value.
Real-World Application
An appraiser reviewing neighborhood sales notices one waterfront sale far above the rest. When describing typical prices in the market analysis, the appraiser reports the median because the waterfront sale inflates the mean.
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