The assessment-to-sale ratios are 0.86, 0.94, 1, 1.06, 1.14. 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) 8.00%
Ordered median=1; absolute deviations are 0.14, 0.06, 0, 0.06, 0.14. Their mean=0.08; COD=0.08/1×100=8%. The unscaled decimal fraction is not the percentage answer.
Why This Is the Correct Answer
Option D is correct because the median of the five ratios is 1.00, and the absolute deviations are 0.14, 0.06, 0, 0.06 and 0.14. These total 0.40, so the average absolute deviation is 0.40 ÷ 5 = 0.08. Then 0.08 ÷ 1.00 × 100 = 8.00%.
Why the Other Options Are Wrong
Option A: 0.08%
Option A, 0.08%, takes the average absolute deviation ratio of 0.08 and labels it a percentage without multiplying by 100. The correct COD is 0.08 ÷ 1.00 × 100 = 8.00%.
Option B: 0.28%
Option B, 0.28%, matches the range of the ratios, 1.14 − 0.86 = 0.28, labeled as a percentage. COD uses the average absolute deviation from the median, 0.08, divided by the median and multiplied by 100, giving 8.00%.
Option C: 10.00%
Option C, 10.00%, divides the deviation sum of 0.40 by 4 (n − 1, as in a sample variance) instead of by all 5 ratios: 0.40 ÷ 4 = 0.10, and 0.10 ÷ 1.00 × 100 = 10.00%. The COD averages over every ratio, so 0.40 ÷ 5 = 0.08 and COD = 8.00%.
Deviate, average, divide, times 100
Find each ratio's distance from the median, average those distances over all the ratios, divide by the median, then multiply by 100.
How to use: Use this four-step sequence to avoid dividing by the wrong count or skipping the final percentage conversion.
Exam Tip
Divide the deviation sum by the full number of ratios, not n − 1, and check that your answer is scaled to a percentage before choosing.
Common Mistakes to Avoid
- -Forgetting to multiply the decimal result by 100
- -Dividing the deviation sum by n − 1 instead of the number of ratios
- -Using the range of the ratios instead of the average absolute deviation
Concept Deep Dive
Analysis
This question tests the coefficient of dispersion (COD) calculation. Find the median ratio, compute each ratio's absolute deviation from it, average those deviations over all the ratios, divide by the median and multiply by 100. Dividing by the wrong count and skipping the final percentage conversion are the usual traps.
Background Knowledge
The COD measures assessment uniformity: how far individual assessment-to-sale ratios typically fall from the median ratio. It is calculated by averaging the absolute deviations from the median over the number of ratios, dividing by the median and multiplying by 100. A lower COD indicates more uniform assessments.
Real-World Application
An assessor's office reviews five recent sales in a neighborhood and computes a COD of 8.00%. The analyst uses this figure to judge how uniform the assessments are compared with the office's performance targets.
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