Coefficient Of Dispersion

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:

 

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 ($362,000) and does the same to the median sale price ($373,000). With these values, he can start using the formula.

 

 

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:

 

 

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%.