Coefficient Of Dispersion


Definition of "Coefficient of Dispersion"

Alicja Whittall real estate agent
Alicja Whittall, Real Estate Agent Keyes Real Estate

The coefficient of dispersion is how municipalities can determine differences between the assessed values of properties in an area or neighborhood. It gives a broader look at the state of the market, and a way to evaluate how consistent the appraisal of the properties is. The definition of the coefficient of dispersion that is used exclusively in dealing with market values and properties is a measure of how much values of a particular variable vary around the mean or median. The end value is represented in percentage from the median.

 

The Coefficient of Dispersion’s formula:

coefficient of dispersion formula 1

 

COD = coefficient of dispersion

N = number of properties in the sample

EPi = appraised value of ith property 

SPi = sale value of ith property

∑ = summation of all the values in the group

 

How to Calculate the Coefficient of Dispersion?

After that insane formula, we understand if homeowners want to stay clear of it, but there are reasons why any homeowner would want to use it. If, for example, you’re house was appraised at a value that is higher than you expect, and the same happened to other neighbors, you can figure out if this is a trend in the area to increase taxes or just the increase of the market value in the area.

Example:

John investigated and managed to find the appraised value of 7 properties around him as well as the actual price for those properties. 

 

Appraised Value

Sales Price

359,000

370,000

362,000

373,000

347,000

358,000

329,000

340,000

384,000

396,000

372,000

386,000

395,000

396,000

 

Now, John finds out the median appraised value by adding all the appraised values, then dividing it by seven properties (364,000) and does the same to the median sale price (374,143). With these values, he can start using the formula.

 

coefficient of dispersion formula 2

 

The median appraised value divided by the median sale value is 0.9729.

John returns to his table to discover the EPi/SPi for each property because the ∑ requires him to discover that value independently for each before he subtracts 0.9729 (the median EPi/SPi) from each:

 

Appraised Value

Sales Price

EPi/SPi

359,000

370,000

0.9702

362,000

373,000

0.9705

347,000

358,000

0.9692

329,000

340,000

0.9676

384,000

396,000

0.9696

372,000

386,000

0.9637

395,000

396,000

0.9974

 

With that out of the way, John needs to subtract 0.9729  from each value. Here he considered negative values positive:

 

Appraised Value

Sales Price

EPi/SPi

EPi/SPi-0.9729

359,000

370,000

0.9702

0.0027

362,000

373,000

0.9705

0.0024

347,000

358,000

0.9692

0.0037

329,000

340,000

0.9676

0.0053

384,000

396,000

0.9696

0.0033

372,000

386,000

0.9637

0.0092

395,000

396,000

0.9974

0.0245

 

Now that he has all the data necessary, John can work the formula:

 

coefficient of dispersion formula 3

 

The coefficient of dispersion is a complex formula but the example above tells us that the average difference the houses have from the median of the assessed sales ratio is 0.75%.

 

 

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