Last updated 2026-07-10
TL;DR
The coefficient of dispersion (COD) measures how uniformly an assessor values properties relative to their actual sale prices. A COD of 0 would mean perfect uniformity; the IAAO standard for residential property is 15.0 or below. A high COD is evidence that assessments in your jurisdiction are unequal, and you can use that fact in an appeal to lower your tax bill.
What does coefficient of dispersion actually mean in plain English?
The coefficient of dispersion tells you how consistent an assessor is across all the properties they value. Specifically, it measures the average percentage deviation of individual assessment-to-sale ratios from the median ratio for the same group of properties. That is a mouthful, so here is the short version: if the COD is 20, the typical property in your area is assessed at a value that is 20 percentage points away from the neighborhood median, on average. Some are over, some are under, and the spread is wide.
It does not tell you whether assessments are high or low overall. That is what the median level of assessment (or median ratio) measures. The COD is purely about consistency. Two jurisdictions could both have a median ratio of exactly 100% (meaning assessors hit the mark on average) while one has a COD of 5 and the other a COD of 35. The first is fair and tight. The second is a mess where some owners pay far too much and others pay far too little, even though the average looks fine.
That distinction matters a lot if you are thinking about an appeal. A high COD is more than an abstract statistic. It is legal ammunition. Many state appeal boards recognize excessive assessment dispersion as independent grounds for relief, separate from whether your individual assessment is too high.
How is the coefficient of dispersion calculated?
The COD calculation has four steps. Work through a simplified example and the math becomes obvious.
Step 1: For each property that sold in the study period, divide the assessed value by the sale price. That ratio is the assessment-to-sale ratio (ASR) for that property. If your home assessed at $300,000 sold for $400,000, the ASR is 0.75, or 75%.
Step 2: Find the median ASR across all properties in the sample. Say the median is 90%.
Step 3: For each property, subtract the median from its individual ASR and take the absolute value (ignore the plus or minus sign). These are the absolute deviations. A property with an ASR of 75% has an absolute deviation of 15 percentage points from the 90% median.
Step 4: Average all those absolute deviations. Then divide by the median and multiply by 100. The formula written out is:
COD = (Mean Absolute Deviation from Median / Median ASR) x 100
The International Association of Assessing Officers (IAAO) defines COD this way in its Standard on Ratio Studies [1]. The result is a percentage. Lower is better. A COD of 10 means the typical property deviates about 10% from the median ratio. A COD of 30 means the spread is enormous.
One subtlety worth knowing: analysts use the median rather than the mean as the center point because the mean is sensitive to a handful of extreme outliers (a teardown that sold for $1 or a mansion that sold to a relative at a steep discount). The median holds up better against those distortions.
What COD is considered acceptable, and what counts as too high?
The IAAO publishes the most widely cited performance standards in property assessment. For single-family residential properties, the IAAO standard is a COD of 15.0 or below [1]. For newer or more homogeneous areas (think cookie-cutter subdivisions built in the last decade), it tightens to 10.0 or below. For income-producing commercial and industrial properties, where valuation gets messier, the acceptable range widens to 20.0 or below.
Here is a quick reference table based on IAAO Standard on Ratio Studies thresholds:
| Property type | Acceptable COD | Notes |
|---|---|---|
| Single-family residential (typical) | 5.0 to 15.0 | Tighter end preferred for homogeneous areas |
| Single-family residential (heterogeneous or rural) | Up to 20.0 | Older, more varied housing stock |
| Vacant land | 5.0 to 25.0 | Wider range reflects sparse sales data |
| Income properties (commercial/industrial) | 5.0 to 20.0 | Complex income-approach valuations allowed more variance |
Many states have written similar thresholds into their own statutes or administrative rules. Massachusetts sets a COD ceiling in its Department of Revenue guidelines for local certification [2]. Illinois uses ratio studies (including COD metrics) in the Property Tax Appeal Board process [3]. When a jurisdiction's COD runs past the acceptable range, the state oversight body can withhold certification of the assessment roll.
For you as an individual appellant, the key number is the COD for your specific property class in your county. A COD of 22 for single-family homes in your county tells a review board that the assessment system is producing wildly unequal results, and that your assessment may well be one of the unlucky high ones.
Where can you find the COD for your county or jurisdiction?
There are three places to look, and they are all free.
First, check your state department of revenue, department of taxation, or property tax division website. Most states run annual or biennial equalization studies that publish ratio study results by county, including COD figures. Examples include the Illinois Department of Revenue's Tentative Multipliers page [3], the Minnesota Department of Revenue's assessment/sales ratio study [4], and the New York State Office of Real Property Tax Services equalization rate data [5].
Second, check your local assessor's own website or annual report. Assessors in higher-performing jurisdictions often publish ratio studies on their own as a transparency measure. If you are researching cook county tax assessor tax bill or similar large urban jurisdictions, the assessor's office typically publishes detailed ratio data.
Third, the IAAO maintains a member directory and some state chapters publish aggregate performance data. Academic researchers have also published peer-reviewed ratio studies for specific metro areas that are publicly available through university repositories.
Cannot find published data? File a public records request with the assessor's office asking for the most recent ratio study or sales ratio analysis. Assessors are generally required to maintain this data. Some will hand it over without question; others will need a formal FOIA request. Either way, the data is a public record in nearly every state.
How does COD connect to coefficient of price-related bias (PRB)?
COD and PRB (price-related bias) are the two main ratio study statistics you will see cited together, and they measure different things.
COD, as covered, measures the spread of assessment ratios, the uniformity question. PRB measures whether expensive properties are systematically assessed at lower ratios than cheap ones, or the reverse. A PRB below -0.05 suggests that high-value properties get a relative break compared to low-value ones, a pattern that shows up again and again in academic research.
A study published in the Journal of Housing Economics found that in many U.S. counties, lower-valued homes are assessed at higher ratios than higher-valued homes, meaning lower-income owners carry a disproportionate share of the property tax burden [6]. The researchers found this regressivity in the majority of the counties they studied. The IAAO's acceptable PRB range is -0.05 to +0.05 [1].
For an individual appeal, PRB matters if your property sits at the lower end of value in your area. If you can show that the assessor's ratio study reveals a negative PRB (high-value properties assessed lower proportionally), and your home is a modest-value property assessed at an above-median ratio, you have two separate strands of argument: your individual assessment is too high, and the systemic pattern explains why.
The two statistics together paint a picture of assessment quality. A jurisdiction with a COD of 8 and a PRB of -0.08 is uniform but regressive. A jurisdiction with a COD of 25 and a PRB of 0.00 is chaotic but not systematically biased. Both are problems. They are just different problems.
Can a high COD help you win a property tax appeal?
Yes, and homeowners leave this argument on the table constantly. Here is how it works in practice.
In most state appeal processes, you have two basic arguments. The first is market value: my property is assessed above its actual fair market value. The second is uniformity or equalization: even if my assessed value is defensible on its own, it is higher than what comparable properties are assessed at, relative to their actual values. Uniformity arguments are grounded in the equal protection principles that run through nearly every state constitution.
A high COD in your jurisdiction is direct evidence that assessments are not uniform. It does not automatically win your appeal, but it shifts the conversation. If the county's own ratio study shows a COD of 28 on residential properties (well above the IAAO threshold of 15), a review board has to reckon with the fact that the assessor's methodology is producing wildly uneven results. Your claim that you landed on the wrong side of that dispersion becomes more credible.
To use COD in an appeal, download the published ratio study data. Note the COD and the median assessment-to-sale ratio for your property class and neighborhood. Calculate your own property's ratio: assessed value divided by your estimate of market value (using recent comparable sales). If your ratio is above the median, you are being assessed more aggressively than your neighbors on average. That gap, combined with a high COD, is a concrete uniformity argument.
Some state appeal boards are more open to statistical arguments than others. At the gwinnett county tax assessor level in Georgia, the Board of Equalization hears uniformity-based arguments regularly. At the bexar county tax assessor level in Texas, the Appraisal Review Board process similarly lets you present evidence of unequal appraisal under Texas Tax Code Section 41.43 [7].
Texas is the most explicit state in the country on this point. Section 41.43 of the Texas Tax Code says a taxpayer is entitled to a reduction if the appraised value exceeds the median appraised value of a comparable set of properties, even if the assessed value is within market range [7]. That is a statutory uniformity right, written into law.
What is the difference between COD and the price-related differential (PRD)?
The price-related differential (PRD) is a third ratio study metric you may run into, distinct from both COD and PRB.
PRD is calculated by dividing the mean (average) ASR by the weighted mean ASR. The weighted mean gives more weight to higher-value properties because it weights each ratio by the sale price. If expensive homes are assessed at lower ratios, the weighted mean will be lower than the simple mean, and the PRD will land above 1.0. An acceptable PRD, per IAAO standards, falls between 0.98 and 1.03 [1].
A PRD above 1.03 signals that lower-value properties are assessed more aggressively than higher-value ones (regressivity). A PRD below 0.98 signals progressivity, the opposite.
In practical terms for an appeal, PRD is less directly actionable than COD because it describes a system-level pattern. COD, by contrast, tells you how much individual dispersion exists, which connects more directly to whether your specific property might be misvalued. Most appellants will lead with COD and comparable sales evidence, then add PRB or PRD data if it backs up a regressivity argument.
How do assessors use COD when setting or defending their assessments?
Assessors care about COD for two reasons: state oversight and professional credibility.
On the oversight side, most states require that local assessment rolls meet ratio study standards before the state will certify the equalization rates used to distribute state aid and calculate tax limits. If a county's COD runs too high for several straight years, the state may impose an equalized multiplier (an across-the-board adjustment factor) or, in extreme cases, take over the reassessment. In Illinois, the state applies county multipliers precisely because many counties fail to self-correct [3].
On the credibility side, assessors who hold their CODs low are showing that their mass appraisal models work. Computer-assisted mass appraisal (CAMA) systems are built partly to pull COD down by applying consistent valuation algorithms. When an assessor upgrades CAMA software or finishes a full reassessment, one of the explicit goals is to drive COD lower.
For la county property tax and other very large jurisdictions, managing COD across millions of parcels is genuinely hard. The sheer volume of property types, the time lag between reassessment cycles, and the mix of neighborhoods all tend to push COD up. That is why the IAAO standard allows slightly wider COD ranges for rural or heterogeneous areas.
One honest caveat: a low COD does not mean every assessment is correct. A jurisdiction where every home is assessed at exactly 120% of market value would have a COD of 0 (perfect uniformity) while every owner is overtaxed. That is why you always check both the COD and the median level of assessment.
What COD data reveals about the fairness of property taxes in the U.S.
The academic literature on assessment quality in America is not encouraging. A 2021 analysis by the Lincoln Institute of Land Policy found that assessment practices vary enormously across states and counties, with many jurisdictions, especially those with infrequent reassessment cycles, showing CODs well above IAAO standards [8].
A widely cited 2017 investigative analysis by the University of Chicago and ProPublica found that in Cook County, Illinois, lower-value properties had assessment ratios roughly double those of higher-value properties, with CODs in some townships topping 30 [9]. That work fed directly into reform efforts in Cook County's assessor's office. This is exactly the kind of documentation that shows COD is not a dry academic metric. It has real distributional consequences.
Nobody has good national data on average CODs by state. The closest systematic picture comes from state ratio study publications. Minnesota, which runs one of the most transparent ratio study programs in the country, publishes annual data showing median residential CODs mostly in the 8 to 14 range for metro counties and higher (sometimes 20+) for rural ones [4]. That pattern, metro areas with tighter CODs and rural areas with wider ones, holds fairly steady across the states that publish this data.
For commercial properties, CODs tend to run higher almost everywhere. Income-approach valuation of commercial property involves more assumptions, more data gaps, and more room for inconsistency. If you own or are assessing commercial real estate in a market like nyc property tax or hennepin county property tax, expect to see COD figures at or near the top of the acceptable range.
How to use COD data in your own property tax appeal
Here is a step-by-step approach a homeowner can actually run without hiring anyone.
First, get the ratio study. Pull the most recent one from your state's department of revenue or your local assessor. Look for your county and your property class (usually single-family residential). Note two numbers: the median ASR and the COD.
Second, calculate your own ASR. Take your assessed value and divide by your best estimate of market value. For market value, use the average sale price of two or three genuinely comparable properties that sold in the last 12 months. If your house assessed at $350,000 and comparable houses sell for $400,000, your ASR is 87.5%.
Third, compare. If the median ASR for your area is, say, 80%, and your ASR is 87.5%, you are assessed at a higher ratio than the median neighbor. That is a uniformity argument.
Fourth, frame it in the appeal. In your written evidence or hearing statement, cite the published ratio study, name the COD (especially if it exceeds the IAAO threshold), state your individual ASR, and note that it sits above the median. You are not asking for perfection. You are asking to be treated like everyone else.
If you want a structured framework for organizing all of this evidence, the TaxFightBack DIY appeal kit walks through the ratio study interpretation step alongside comparable sales analysis, so you build a complete argument rather than a one-dimensional one. The kit is designed for homeowners who want to keep 100% of their savings instead of paying a contingency firm.
For large, complex jurisdictions like montgomery county property tax in Maryland or santa clara property tax in California, published ratio studies run particularly detailed and are worth the hour it takes to find them.
Are there limits to what COD can tell you?
COD is a strong diagnostic, but it has real limits you should know before leaning on it.
It depends on sales sample quality. If very few properties sold in your neighborhood during the study period, the COD calculation can be statistically unreliable. A COD of 30 based on six sales is much weaker evidence than a COD of 30 based on 600 sales. Some county ratio studies note the sample size. If they do not, ask.
It is a snapshot. The COD in a published study reflects sales and assessments from a prior period, sometimes two or three years old in states with infrequent reassessment cycles. Real estate markets move fast, and a study from a 2022 assessment roll may not reflect 2024 or 2025 conditions.
It describes the distribution, not your individual situation. Even in a jurisdiction with a COD of 8 (very uniform), your specific property could still be badly over-assessed because of a data error, an incorrect property characteristic, or a unique market factor. Do not skip the comparable sales analysis just because the COD looks fine. The COD tells you about the system. The comps tell you about your house.
And some appeal boards are skeptical of statistical arguments from unrepresented homeowners. A board used to hearing appraisers say "comparables support a value of X" may be less comfortable with a homeowner citing IAAO standard thresholds. That does not mean you should skip it. It means you lead with the comparable sales evidence and use the COD data as supporting context, not your sole argument.
For complex commercial properties where statistical arguments carry more weight, hiring a commercial appraiser familiar with ratio studies may be worth the cost. For single-family homes, doing it yourself with good comp evidence and COD context is very achievable.
Frequently asked questions
What is a good coefficient of dispersion for property assessments?
The IAAO sets 15.0 as the upper limit for single-family residential properties in typical markets, and 10.0 for more homogeneous areas like newer subdivisions. For commercial and industrial properties, 20.0 is the ceiling. Any COD within those ranges is considered acceptable. Below 10 for residential is excellent. Above the ceiling indicates assessment inequity that may be grounds for an appeal.
Is a high COD enough to win a property tax appeal on its own?
Rarely on its own, but it is meaningful supporting evidence. A COD above the IAAO standard tells a review board the assessment system is producing unequal results. Pair it with a showing that your individual assessment-to-sale ratio sits above the median ratio for your area, and you have a concrete uniformity argument. Most successful appeals combine the statistical argument with comparable sales evidence showing market value is lower than assessed value.
What is the difference between COD and median assessment ratio?
The median assessment ratio (or level of assessment) tells you whether properties are assessed above or below market value on average. The COD tells you how consistent that assessment is across individual properties. A jurisdiction could have a perfectly calibrated median ratio of 100% while carrying a COD of 30, meaning some owners are massively over-assessed and others under-assessed even though the average looks correct. You need both numbers to understand your situation.
Where does the IAAO's COD standard of 15% for residential property come from?
The IAAO (International Association of Assessing Officers) published its Standard on Ratio Studies, which sets performance benchmarks based on research into what levels of dispersion are achievable given practical constraints in mass appraisal. The 15% ceiling for residential property reflects a balance between theoretical precision and real-world data limitations. The standard has been updated periodically; the current version is available directly from the IAAO at iaao.org.
How is COD different from coefficient of variation (CV)?
Both measure spread, but COD uses the median as its center point and takes the mean absolute deviation. The coefficient of variation uses the mean as its center and measures standard deviation relative to the mean. COD is preferred in ratio studies because property sale prices have outliers that distort the mean. Using the median keeps COD steadier when a handful of unusual sales could otherwise skew the whole calculation.
Can I calculate the COD for my own neighborhood?
Yes, if you have enough comparable sales data. Collect recent sales in your neighborhood, calculate an assessment-to-sale ratio for each, find the median ratio, then compute each property's absolute deviation from that median, average those deviations, and divide by the median. Multiply by 100 for the COD. In practice you need at least 20 to 30 sales for a reliable result. County assessor sales databases or public MLS data are your best sources.
Does a low COD mean my assessment is correct?
Not necessarily. A low COD means assessments are consistent with each other, not that they are accurate relative to true market value. If every property in a jurisdiction is uniformly assessed at 130% of market value, the COD could be near zero while every owner is overtaxed. That is why you always check the median level of assessment alongside the COD. Uniformity and accuracy are separate questions.
What states publish COD data for every county?
Minnesota, Illinois, Massachusetts, and New York are among the states with the most transparent annual ratio study publications that include COD by county and property class. Texas appraisal districts are studied by the Texas Comptroller of Public Accounts, which publishes property value study results including ratio statistics. Many other states publish summary-level data without full county breakdowns. Check your state's department of revenue or taxation website.
How do assessors reduce COD between reassessment cycles?
The main tools are more frequent reassessments, better computer-assisted mass appraisal (CAMA) models, and improved sales verification to ensure only arm's-length transactions are used in ratio studies. Some jurisdictions also apply statistical smoothing to catch outlier assessments before the roll is finalized. Updating property characteristic data (square footage, condition, permits) also reduces model errors that add to dispersion.
Does COD matter for commercial property appeals?
Yes, and arguably more so. Commercial property assessments have naturally higher CODs because income-approach valuation requires more assumptions. The IAAO allows a COD up to 20 for commercial properties. If your jurisdiction's commercial COD exceeds that, and your property's assessment-to-income-value ratio sits above the median, you have a strong uniformity argument. For large commercial properties, engaging an MAI-certified appraiser to run the ratio analysis alongside an income approach is usually worth the cost.
What is the price-related bias (PRB) and how does it relate to COD?
PRB measures whether high-value properties are assessed at systematically lower ratios than low-value ones (regressivity) or the reverse. COD measures overall spread without distinguishing by value. The IAAO acceptable PRB range is -0.05 to +0.05. If your jurisdiction has a negative PRB, lower-value homes are assessed proportionally higher, which compounds whatever dispersion the COD reveals. Both statistics together give a fuller picture of assessment quality than either alone.
Can I use COD data if I'm appealing in Texas under the unequal appraisal rule?
Yes. Texas Tax Code Section 41.43 gives property owners the explicit right to appeal on the basis of unequal appraisal, meaning your property is appraised higher than a median of comparable properties adjusted for differences. The Texas Comptroller's property value study publishes ratio statistics for every appraisal district. A COD well above IAAO standards in your district strengthens the context for your Section 41.43 argument, though the direct evidence is a comparison of your ratio to the median for comparable properties.
How often are ratio studies and COD data updated?
It varies by state. Minnesota and Massachusetts publish annual studies. Illinois publishes tentative multiplier data annually. Some states run studies only every two or three years, which can leave your COD data stale relative to current market conditions. Always note the study year when you cite the data in an appeal, and be ready for a board to question whether conditions have shifted since the study was conducted.
Sources
- International Association of Assessing Officers (IAAO), Standard on Ratio Studies: IAAO sets COD standards of 5.0-15.0 for single-family residential, up to 20.0 for commercial/industrial, and acceptable PRD range of 0.98-1.03; PRB acceptable range is -0.05 to +0.05
- Massachusetts Department of Revenue, Division of Local Services, Assessment/Sales Ratio Guidelines: Massachusetts DOR sets COD ceilings in guidelines for local assessment certification
- Illinois Department of Revenue, Property Tax and Equalization: Illinois uses ratio studies including COD metrics and applies county equalization multipliers where jurisdictions fail to self-correct
- Minnesota Department of Revenue, Assessment/Sales Ratio Study: Minnesota publishes annual ratio studies showing residential CODs mostly 8-14 for metro counties and higher (sometimes 20+) for rural ones
- New York State Office of Real Property Tax Services, Equalization Rate Data: New York publishes equalization rate data derived from ratio studies at the county and municipal level
- Avenancio-León & Howard, 'The Assessment Gap: Racial Inequalities in Property Taxation', Journal of Housing Economics: Study found lower-valued homes are assessed at higher ratios than higher-valued homes in the majority of U.S. counties studied, indicating regressive assessment patterns
- Texas Tax Code Section 41.43, Unequal Appraisal: Texas Tax Code Section 41.43 entitles property owners to relief if appraised value exceeds the median appraised value of comparable properties, codifying a statutory uniformity right
- Lincoln Institute of Land Policy, 'Rethinking the Property Tax' research series: 2021 analysis found assessment practices vary enormously across states and counties, with many jurisdictions showing CODs well above IAAO standards, especially those with infrequent reassessment cycles
- ProPublica / University of Chicago, 'The Tax Divide' Cook County assessment analysis (2017): Analysis found that in Cook County, Illinois, lower-value properties had assessment ratios roughly double those of higher-value properties, with CODs in some townships exceeding 30
- Texas Comptroller of Public Accounts, Property Value Study: Texas Comptroller publishes annual property value study including ratio statistics for every appraisal district, used in Section 41.43 unequal appraisal appeals