A ratio study has an arithmetic mean assessment-to-sale ratio of 1.02 and a sale-price-weighted mean ratio of 1. Compute PRD = arithmetic mean ÷ weighted mean; report three decimals.
Correct Answer
D) 1.020
1.02/1=1.02. This is a descriptive point statistic; it does not alone prove assessment bias or a legal compliance finding.
Why This Is the Correct Answer
Option D is correct because PRD = arithmetic mean ÷ weighted mean = 1.02 ÷ 1 = 1.020. This is a descriptive point statistic; by itself it does not prove assessment bias or establish a legal compliance finding.
Why the Other Options Are Wrong
Option A: 0.980
Option A, 0.980, comes from inverting the division (1 ÷ 1.02 = 0.980). The PRD puts the arithmetic mean on top: 1.02 ÷ 1 = 1.020.
Option B: 0.020
Option B, 0.020, reports only the amount by which the PRD exceeds 1 (1.02 − 1). The PRD itself is 1.02 ÷ 1 = 1.020.
Option C: 1.000
Option C, 1.000, is the weighted mean ratio, reported instead of the PRD. Dividing the arithmetic mean by it gives 1.02 ÷ 1 = 1.020.
Mean on top, weighted below
Write PRD as a fraction with the plain mean as the numerator and the weighted mean as the denominator.
How to use: Use this to avoid inverting the PRD formula.
Exam Tip
When the weighted mean is 1, the PRD equals the arithmetic mean. Distractors often show the inverse or the difference from 1.
Common Mistakes to Avoid
- -Inverting the PRD formula
- -Reporting only the excess over 1
- -Reporting one of the input means as the PRD
Concept Deep Dive
Analysis
This question tests a direct PRD calculation from two given means. PRD is the arithmetic mean ratio divided by the weighted mean ratio. Since the weighted mean is 1, the PRD equals the arithmetic mean.
Background Knowledge
The PRD is calculated by dividing the mean ratio by the weighted mean ratio. A PRD above 1 means the simple mean exceeds the weighted mean, suggesting that higher-priced properties tend to have lower ratios in the sample. Interpreting the figure in a population or legal sense requires more evidence than a single point value.
Real-World Application
An assessment analyst reports a mean ratio of 1.02 and a weighted mean ratio of 1.00 for a neighborhood. The PRD of 1.020 is noted for review alongside other ratio-study statistics.
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Which statistic does the IAAO standard describe as a measure of uniformity between high- and low-value properties, computed with the weighted mean?
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The first quartile of sale prices is $420,000 and the third quartile is $580,000. Compute the quartile coefficient of dispersion (Q3−Q1)/(Q3+Q1), as a decimal to three places.