For positive assessment-to-sale ratios, define COD as 100 × mean absolute deviation from their median ÷ median. How does it differ from the median ratio?
Correct Answer
A) The median describes the central ratio level; COD describes relative dispersion
The median describes the center of the observed assessment-to-sale ratios. COD, defined here as 100 times their mean absolute deviation from the median divided by that median, describes relative dispersion. A centered distribution may have widely varying spread; the two statistics are not interchangeable. Neither normality nor centering alone makes them equal.
Why This Is the Correct Answer
Option A is correct because the median describes the central level of the assessment-to-sale ratios. The COD, 100 times the mean absolute deviation from the median divided by the median, describes relative dispersion. A set of ratios can be well centered yet widely spread, so both statistics are needed.
Why the Other Options Are Wrong
Option B: Both describe only the center and are interchangeable
Option B, saying both describe only the center and are interchangeable, is wrong because the COD measures spread, not center. The two statistics answer different questions.
Option C: COD is the central ratio of the sample; the median measures the spread of ratios
Option C reverses the roles, calling the COD the central ratio and the median the spread. The median is the measure of central level and the COD is the measure of dispersion.
Option D: Normality requires the median and COD to be equal
Option D, saying normality requires the median and COD to be equal, is incorrect; they measure different things on different scales, and neither normality nor centering makes them equal.
Median where, COD how scattered
The median tells you where the ratios sit; the COD tells you how scattered they are.
How to use: Use this to sort ratio-study statistics into level measures and uniformity measures.
Exam Tip
When an option swaps the roles of a level measure and a dispersion measure, eliminate it.
Common Mistakes to Avoid
- -Treating the COD as a measure of central tendency
- -Assuming a well-centered median means uniform assessments
- -Thinking the median and COD can be compared directly as equals
Concept Deep Dive
Analysis
This question tests the difference between a measure of level and a measure of dispersion. The median ratio tells you where the ratios are centered; the COD tells you how widely they spread around that center. The two answer different questions and cannot replace each other.
Background Knowledge
Ratio studies measure appraisal level with statistics such as the median, mean and weighted mean ratios, and measure uniformity with statistics such as the COD. A complete analysis looks at both because accurate average levels can hide poor uniformity.
Real-World Application
An appraiser reviewing a jurisdiction finds a median ratio near 1.00 but a high COD. The appraiser explains that assessments are right on average but individual properties vary widely, so some owners are over-assessed and others under-assessed.
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Previous Question
The assessment-to-sale ratios are 0.8, 0.85, 0.9, 0.92, 0.95, 0.98, 1.02, 1.05, 1.08, 1.1, 1.15, 1.2. 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.
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