Which statistic does the IAAO standard describe as a measure of uniformity between high- and low-value properties, computed with the weighted mean?
Correct Answer
C) The price-related differential
The weighted mean is used in computing the price-related differential (PRD), a measure of uniformity between high- and low-value properties.
Why This Is the Correct Answer
Option C is correct because the IAAO standard describes the weighted mean as being used in computing the price-related differential (PRD), a measure of uniformity between high- and low-value properties. The PRD compares the simple mean ratio with the weighted mean ratio to reveal whether ratios vary with property value.
Why the Other Options Are Wrong
Option A: The coefficient of dispersion
Option A, the coefficient of dispersion, measures the average deviation of ratios around the median ratio. It describes overall uniformity among properties, not uniformity between high- and low-value properties computed with the weighted mean.
Option B: The median ratio
Option B, the median ratio, is a measure of the overall assessment level. It indicates central tendency, not uniformity between high- and low-value properties.
Option D: The coefficient of variation
Option D, the coefficient of variation, expresses the standard deviation relative to the mean. It measures relative dispersion and does not use the weighted mean to compare high- and low-value properties.
PRD: Price-Related means price levels
The Price-Related Differential is the statistic that relates ratios to price, comparing high-value and low-value properties.
How to use: Use this to match the PRD to questions about equity between high- and low-value properties.
Exam Tip
Link the phrases 'weighted mean' and 'high- and low-value properties' to the PRD; link 'around the median' to the COD.
Common Mistakes to Avoid
- -Confusing the PRD with the COD
- -Treating the median ratio as a uniformity measure
- -Thinking the coefficient of variation uses the weighted mean
Concept Deep Dive
Analysis
This question tests recognition of the ratio-study statistic tied to the weighted mean and to uniformity between high- and low-value properties. The price-related differential uses the weighted mean in its calculation and measures vertical equity. Other ratio-study statistics measure overall level or general dispersion instead.
Background Knowledge
Ratio studies use measures of level (such as the median and mean ratios), measures of uniformity among properties (such as the COD), and measures of uniformity between high- and low-value properties (such as the PRD). The weighted mean ratio gives more influence to higher-priced sales, which is why comparing it with the simple mean reveals value-related bias.
Real-World Application
A county reviewing its assessment roll wants to know whether expensive homes are assessed at lower ratios than modest homes. Its analysts compute the PRD, which uses the weighted mean, to measure that vertical uniformity.
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