Definition of "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 (364,000) and does the same to the median sale price (374,143). 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%.
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