The assessment-to-sale ratios are 0.9, 0.95, 1.05, 1.1. Calculate COD as [average absolute deviation from the median ÷ median]×100. For even n, average the two middle ratios. Report the COD as a percentage to two decimals.
Correct Answer
D) 7.50%
Ordered median=1; absolute deviations are 0.1, 0.05, 0.05, 0.1. Their mean=0.075; COD=0.075/1×100=7.5%. The unscaled decimal fraction is not the percentage answer.
Why This Is the Correct Answer
Option D is correct because the median is 1.00, the absolute deviations sum to 0.30 and average 0.30 / 4 = 0.075, and COD = 0.075 / 1.00 × 100 = 7.50%. Multiplying by 100 expresses the result as a percentage.
Why the Other Options Are Wrong
Option A: 0.08%
Option A, 0.08%, is the unscaled average deviation of 0.075, rounded to 0.08, with a percent sign attached. COD multiplies by 100, giving 0.075 × 100 = 7.50%.
Option B: 0.20%
Option B, 0.20%, matches the range of the ratios, 1.10 − 0.90 = 0.20, which is not part of the COD formula. COD = (0.30 / 4) / 1.00 × 100 = 7.50%.
Option C: 7.89%
Option C, 7.89%, uses the lower middle ratio, 0.95, as the median instead of averaging the two middle ratios. The deviations from 0.95 still average 0.30 / 4 = 0.075, but 0.075 / 0.95 × 100 = 7.89%; with the correct median of 1.00, COD = 7.50%.
Even count, average middles
With an even number of ratios, average the two middle values to get the median before measuring deviations.
How to use: Use this before computing COD on an even-sized set of ratios.
Exam Tip
With an even count, average the two middle ratios for the median, then divide the deviation sum by all the ratios and multiply by 100.
Common Mistakes to Avoid
- -Leaving the result as a decimal instead of a percentage
- -Using one middle value instead of averaging the two for an even count
- -Using the range of the ratios in place of the average absolute deviation
Concept Deep Dive
Analysis
This question tests calculating the COD for an even number of ratios. The median of 0.90, 0.95, 1.05 and 1.10 is (0.95 + 1.05) / 2 = 1.00, not either middle value alone. The absolute deviations are 0.10, 0.05, 0.05 and 0.10, averaging 0.075, so COD = 0.075 / 1.00 × 100 = 7.50%.
Background Knowledge
The coefficient of dispersion is the average absolute deviation from the median, divided by the median and multiplied by 100. With an even number of ratios, the median is the average of the two middle values. COD is a primary measure of assessment uniformity in ratio studies.
Real-World Application
An assessor checks four sales in a small condominium complex and finds a COD of 7.50%. The assessor notes the small sample before drawing conclusions about uniformity.
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