The assessment-to-sale ratios are 0.9, 0.94, 0.98, 1.02, 1.06, 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
C) 6.00%
Ordered median=1; absolute deviations are 0.1, 0.06, 0.02, 0.02, 0.06, 0.1. Their mean=0.06; COD=0.06/1×100=6%. The unscaled decimal fraction is not the percentage answer.
Why This Is the Correct Answer
Option C is correct because the two middle ratios, 0.98 and 1.02, average to a median of 1.00. The absolute deviations are 0.10, 0.06, 0.02, 0.02, 0.06 and 0.10, which total 0.36 and average 0.36 / 6 = 0.06. Then 0.06 / 1.00 × 100 = 6.00%.
Why the Other Options Are Wrong
Option A: 0.06%
Option A, 0.06%, reports the unscaled average deviation ratio (0.06 / 1.00) with a percent sign but without multiplying by 100. The COD is 0.06 × 100 = 6.00%.
Option B: 0.20%
Option B, 0.20%, matches the range of the ratios (1.10 − 0.90 = 0.20) left unscaled, which is not the COD. The COD averages the absolute deviations (0.36 / 6 = 0.06) and scales by 100 to give 6.00%.
Option D: 7.20%
Option D, 7.20%, divides the 0.36 total deviation by 5 (n − 1, as in a sample variance) instead of by all 6 ratios: 0.36 / 5 = 0.072, times 100 = 7.20%. Correctly, 0.36 / 6 = 0.06, and 0.06 / 1.00 × 100 = 6.00%.
Decimal times hundred equals percent
The COD formula ends with ×100, so an average deviation of 0.06 over a median of 1.00 becomes 6 percent.
How to use: Use this reminder to check that your COD answer is scaled as a percentage before choosing.
Exam Tip
If one choice is exactly one-hundredth of another, the smaller one usually skipped the ×100 step; also confirm you divided the deviation sum by the full count of ratios.
Common Mistakes to Avoid
- -Leaving the result as a decimal instead of a percentage
- -Dividing the total deviation by n − 1 instead of the number of ratios
- -Using the range in place of the average absolute deviation
Concept Deep Dive
Analysis
This question tests a full COD calculation with an even number of ratios. You average the two middle ratios to get the median, find each absolute deviation, average them over all six ratios, divide by the median and multiply by 100. The distractors come from failing to scale to a percentage, using the range, or dividing by the wrong count.
Background Knowledge
The COD expresses the average absolute deviation from the median as a percentage of the median. It is the standard uniformity measure in ratio studies; the deviations are averaged over the number of ratios, and the final multiplication by 100 converts the decimal into a percentage.
Real-World Application
An appraiser checking a jurisdiction's assessment uniformity for six sales computes a COD of 6.00%. That indicates the ratios deviate from the median by an average of 6 percent, which the appraiser compares against the uniformity expectations stated for the study.
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Previous Question
Sale prices are $270,000, $290,000, $300,000, $310,000, $330,000. Treat the listed observations as the complete population and divide by n when computing the standard deviation. Report to the nearest dollar.
Next Question
The base-period median sale price is $400,000 and the current-period median is $460,000. Compute the price relative defined as current ÷ base, as a decimal to three places.