Adding one unusually high sale to a data set will have what effect?
Correct Answer
A) It moves the mean substantially while the median shifts little, if at all
Why this is correct: The mean is computed from every value in the set, so an unusually high sale enters the sum directly and pulls the average up by the amount it exceeds the old mean, divided by the new count. The median depends only on position in the ordered list. Adding one observation does move the middle position, so the median can shift to the next value up, but it moves only as far as the neighboring data point and never toward the outlier itself. In a data set of any size the mean moves substantially and the median moves slightly or not at all. Why the other choices are wrong: 'It moves the median and leaves the mean unchanged' reverses the two; the mean is the measure that cannot ignore any value. 'It moves both measures by the same dollar amount' would require the median to respond to magnitude, which it does not; the median only counts positions. 'It leaves both measures completely unaffected' ignores that the mean is recomputed from a changed sum and a changed count. Exam tip: Mean is sensitive to magnitude, median is sensitive only to order. In a skewed set of sales, the median is the more representative central measure.
Why This Is the Correct Answer
Adding one high sale changes both the sum and the count, so the mean is recomputed and rises by the outlier's excess over the old mean divided by the new number of observations. The median shifts by at most one position in the ordered list, which moves it only as far as the neighboring value, and in an even-to-odd transition it may not move at all. The mean therefore moves substantially while the median shifts little, if at all.
Why the Other Options Are Wrong
Option B: It moves the median and leaves the mean unchanged
This reverses the two measures. The mean cannot be unchanged, because it is arithmetically derived from every observation including the new one. The median is the measure with the capacity to stay put.
Option C: It moves both measures by the same dollar amount
For both to move by the same dollar amount, the median would have to respond to the outlier's magnitude, and it does not. The median only registers that one more observation now sits above the middle. Equal movement would be a coincidence, not a rule.
Option D: It leaves both measures completely unaffected
The mean is recomputed from a larger sum over a larger count, so it necessarily changes unless the new sale happens to equal the old mean, which an unusually high sale by definition does not. Treating both measures as inert ignores how an average is built.
Money moves the mean
Money moves the mean; position places the median. The mean asks how much, the median asks how many are above and below. An outlier is a big how much and a single how many.
How to use: When a question adds or removes an extreme value, ask what each measure looks at. Anything that changes magnitude hits the mean hard; only something that changes the count meaningfully nudges the median.
Exam Tip
Beware absolute words in statistics options. 'Unchanged' and 'unaffected' are rarely exactly true, and the best answer is usually the one that describes the size of the effect rather than denying it.
Common Mistakes to Avoid
- -Assuming the median is completely immune to a new observation
- -Using the mean to describe a visibly skewed set of sales
- -Reporting a central tendency without noting the dispersion around it
Concept Deep Dive
Analysis
Measures of central tendency differ in what information they use. The mean uses every value's magnitude, so each observation exerts leverage proportional to how far it sits from the current average. The median uses only rank order, so a value's size beyond its position is irrelevant: a sale at $900,000 and a sale at $9,000,000 occupy the same slot in the ordered list. That difference is what makes the median resistant to outliers and the mean sensitive to them, and it is why appraisers report the median sale price for a skewed market and the mean for a tight, symmetrical one.
Background Knowledge
You need the definitions of mean, median and mode and the idea of resistance to outliers. You also need to recognize skew: in a market with a few very expensive sales, the mean sits above the median, and the gap between them is itself a diagnostic of how skewed the data are.
Real-World Application
A neighborhood's twenty-two closings include one waterfront estate at triple the next highest price. The appraiser reports the median as the representative sale price and notes the mean separately, so a lender is not misled about what a typical house in the market brings.
More Statistics Questions
A set of comparable sales has a mean of $250,000 and a standard deviation of $20,000. What is the coefficient of variation?
A property sold for $400,000 and resold three years later for $463,050 with no physical change. What compound annual rate does this indicate?
A histogram of neighborhood sale prices shows two distinct peaks. What does this most likely mean?
What does it mean to validate a regression model?
In a market study, what does a frequency distribution of sale prices show?
An appraiser includes months elapsed since each sale as a variable in a price model. What is this intended to capture?
An appraiser presents a statistical analysis in a report. What must accompany it for the reader to weigh it?
An R-squared of 0.86 in a sales model indicates that:
Which measure would best summarize the most common lot size in a subdivision?
Paired sales analysis and regression differ mainly in that regression:
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