Reader Susan Handelsman found this explanation on Nunda Township web site.  Assessor Mark Dzemske informs me it was written in 2001 by former Supervisor John Heisler.

This is good explanation from Nunda Township Assessment website:

Coefficient of Dispersion . . . . . What is it?

How do we judge the Assessor’s job?

Well, the Township Assessor must certify the assessed valuation of each and every parcel in the Township.

This certification is reported to the McHenry County Supervisor of Assessments and used to create your tax bill.

There are over 18,400 parcels in Nunda Township.

How do we measure the Assessor’s performance?

We measure it “statistically”.

There are basically 2 statistics that we need to measure.

How close to the statutory 33 1/3% of fair market value are the Assessments; and how uniform are our assessments.

The most commonly used statistical measure of assessment uniformity in a ratio study is the COEFFICIENT OF DISPERSION (COD).

The COD provides a measure of the variation of individual assessment ratios around the median level of assessment.

It can be stated as the “average error” expressed as a percentage.

The lower the rate of dispersion, the more uniform, and fair the spread of the tax burden.

To put it another way, there should be some uniformity in the assessment of all the homes in your neighborhood, even if they don’t look exactly like yours.

The COD actually measures that uniformity; or lack of uniformity in statistical terms.

Once we calculate the median, or the middle, we can determine how wide are the variations from the median.

How fair is your assessment as compared to your neighbors?

We calculate this variation on a Township wide basis, neighborhood by neighborhood.

What is this “Median Level of Assessment”?

Well we all know the state statute says the assessed valuation of your home should be 33.3% of fair market value.

The fair market value can only be determined by a sale.

So, we list the sales, divide each sales price by the Assessed Valuation and see how close they all came to 33.3%. How wide are the variations from the median, or middle? How “uniform” are our assessments. . . . .

What is our Coefficient of Dispersion ?

To put it another way.

What is the average deviation?

Assume a township has a median level of assessment of 30% and a Coefficient of Dispersion of 40%.

The assessment levels of individual properties on the average can be expected to deviate plus or minus 40% from the middle.

Assume two similar properties had a market value of $90,000.

One could be assessed at 42% and the other at 18%.

Given a tax rate of 6%, one property tax bill could be $972 while the other $2,268.

The tax burden is not shared equally in this example.

You can see how important assessment uniformity can be.

Each Township Assessor strives for a low COD.

The lower the COD, the smaller the Average Deviation.

Our County Supervisor of Assessments considers any Township under 15% to be good and any Township over 20% to be bad.

Adjustments to the Township Assessors books or even rejection may be the result of a high COD.