A ratio sample includes one extreme ratio caused by a data error. Which measure of appraisal level is resistant to it, so that trimming would not be required?
Correct Answer
D) The median ratio
Some statistical measures, such as the median ratio, are resistant to the influence of outliers, and trimming would not be required for them.
Why This Is the Correct Answer
Option D is correct because the median ratio depends on the middle position of the ordered ratios, not on the size of the extreme values. One extreme ratio caused by a data error barely affects which ratio sits in the middle. For that reason the median is resistant to outliers, and trimming would not be required for it.
Why the Other Options Are Wrong
Option A: The mean ratio
Option A, the mean ratio, adds every ratio and divides by the count, so one extreme ratio pulls it up or down. It is not resistant to outliers.
Option B: The weighted mean ratio
Option B, the weighted mean ratio, also sums every ratio's contribution, here weighted by sale price. An extreme ratio, especially on a high-priced sale, can shift it noticeably.
Option C: The coefficient of variation
Option C, the coefficient of variation, is a measure of dispersion rather than appraisal level, and because it is based on squared deviations it is especially sensitive to an extreme ratio.
Median sits in the middle
An outlier lives at the end of the line, and the median only cares who stands in the middle.
How to use: Use this image when a question asks which statistic resists extreme values.
Exam Tip
First separate measures of level (median, mean, weighted mean) from measures of spread (COD, COV) before choosing.
Common Mistakes to Avoid
- -Choosing a dispersion measure when the question asks about appraisal level
- -Assuming the weighted mean is resistant because it is weighted
- -Thinking every measure must be trimmed when outliers appear
Concept Deep Dive
Analysis
This question tests which measure of appraisal level resists the influence of an outlier. Measures that add up every ratio's magnitude move when one value is extreme, while a measure based on position in an ordered list does not. Note also that one choice is a dispersion measure, not a level measure at all.
Background Knowledge
Ratio studies calculate several measures of appraisal level, including the median, mean and weighted mean ratios. The median divides the data into two equal parts and is less affected by extreme ratios than the other measures, which is why outlier trimming matters less for it.
Real-World Application
An appraiser analyzing assessment ratios finds one sale with a ratio of 3.5 caused by a keying error in the price. The mean ratio jumps noticeably, but the median barely moves, so the appraiser relies on the median while correcting the data.
More Statistics Questions
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An appraiser estimates a market-wide price trend using only sales data from one brokerage that specializes in luxury homes, without checking how other segments are represented. What is the principal concern?
Compared with analyzing one matched sale pair for one feature, what can a suitably specified multiple regression do?
The base-period median sale price is $400,000 and the current-period median is $460,000. Compute the price relative defined as current ÷ base, as a decimal to three places.
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Assessment-to-sale ratios are 0.94, 0.96, 0.98, 1, 1.01. Compute the arithmetic mean. Report as a decimal ratio to three places.
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Previous Question
Assessment-to-sale ratios are 1.1, 1, 0.9; corresponding sale prices are $100,000, $200,000, $500,000 in the same order. Compute PRD as the arithmetic mean ratio divided by the sale-price-weighted mean ratio. Round to two decimals.
Next Question
Four parcels have assessment-to-sale ratios of 1.15 on $90,000; 1.05 on $150,000; 0.98 on $250,000; and 0.92 on $400,000. Define PRD as the unweighted mean ratio divided by the sale-price-weighted mean ratio. Which rounded PRD and descriptive sample tendency are consistent with these data?