The assessment-to-sale ratios are 0.9, 0.95, 1, 1.05, 1.15. 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
A) 7.00%
Ordered median=1; absolute deviations are 0.1, 0.05, 0, 0.05, 0.15. Their mean=0.07; COD=0.07/1×100=7%. The unscaled decimal fraction is not the percentage answer.
Why This Is the Correct Answer
Option A is correct because the median of 0.90, 0.95, 1.00, 1.05 and 1.15 is 1.00. The absolute deviations are 0.10, 0.05, 0, 0.05 and 0.15, which sum to 0.35 and average 0.35 ÷ 5 = 0.07. COD = 0.07 ÷ 1.00 × 100 = 7.00%.
Why the Other Options Are Wrong
Option B: 0.07%
Option B, 0.07%, reports the unscaled average deviation 0.07 as a percentage without multiplying by 100. The COD is 0.07 ÷ 1.00 × 100 = 7.00%.
Option C: 0.25%
Option C, 0.25%, matches the range of the ratios (1.15 − 0.90 = 0.25), not the average absolute deviation, and it is not scaled to a percentage. The COD is 0.07 ÷ 1.00 × 100 = 7.00%.
Option D: 8.75%
Option D, 8.75%, divides the sum of absolute deviations by 4 instead of 5, leaving out the median's zero deviation: 0.35 ÷ 4 = 0.0875, and 0.0875 ÷ 1.00 × 100 = 8.75%. All five ratios count, so the average deviation is 0.35 ÷ 5 = 0.07 and COD = 7.00%.
Average gap over median
COD is the average gap from the median, divided by the median, times 100. A tiny decimal with a percent sign usually means the times-100 step was skipped.
How to use: Use this to check the scale of your COD answer.
Exam Tip
Divide the sum of deviations by the number of ratios, including the median's zero deviation, and remember to multiply by 100.
Common Mistakes to Avoid
- -Reporting the unscaled decimal as a percentage
- -Using the range of ratios instead of the average deviation
- -Leaving the median's zero deviation out of the count
Concept Deep Dive
Analysis
This question tests the coefficient of dispersion for an odd number of ratios. Find the median of the five ordered ratios, compute absolute deviations from it, average them, divide by the median and multiply by 100.
Background Knowledge
The coefficient of dispersion is the average absolute deviation from the median divided by the median and expressed as a percentage. It is a common measure of assessment uniformity in ratio studies. With an odd number of ratios, the median is the middle ordered value.
Real-World Application
An assessment reviewer tests five recent sales and finds a COD of 7.00%. This indicates assessed values are fairly uniform relative to sale prices in that group.
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