# Coefficient of Dispersion: Definition & Formula

Instructor: Janice Chretien
The coefficient of dispersion is a ratio that the International Association of Assessing Officers uses to evaluate consistency or volatility in the assessed value of real property in a particular neighborhood or area.

## Accurate Appraisals?

Jill, Steve, and Raj were visiting before the quarterly home owner's association meeting. The topic of discussion was the consistent increase in property taxes over the past three years.

Raj pointed out that it is not the tax rate that is going up but the assessed value of their properties that the district has increased each year. Jill said, ''I don't think I got a fair assessment. If I could sell my home for what the tax district says it is worth, I would sell!''

Steve replied, ''I understand how you feel, Jill. I was a bit shocked when I saw my assessed value, so I did an analysis called the coefficient of dispersion to investigate the fairness of the district's appraised value of my property.'' With that, Steve began to explain the coefficient of dispersion.

## The Coefficient of Dispersion Formula

The coefficient of dispersion (COD) is the average difference a group of numbers has from the median. The value is reported as a percentage of the median. In ratio studies, the coefficient of dispersion is reported as an average percentage difference from the median ratio. The formula is as follows:

EPi is the expected price of ith property. SPi is the sales price of the ith property.

Steve obtained the appraised value and sales price for the properties in the neighborhood:

Appraised Value Sales Price
671,998 749,999
689,322 755,000
734,653 784,500
794,276 819,500
829,276 839,999
939,710 950,000
947,251 964,999

The median appraised value is \$794,276, and the median sales price is \$819,500. Using this information, Steve began to plug in the formula.

The median EPi / SPi = 0.9692

Steve drew a spreadsheet to illustrate. Since the formula is for the absolute value, consider negative numbers to be positive.

Appraised Value Sales Price EPi / SPi
689,322 755,000 0.8960
689,322 755,000 0.9130
734,653 784,500 0.9365
794,276 819,500 0.9692
829,276 839,999 0.9872
939,710 950,000 0.9892
947,251 964,999 0.9816

Next, Steve calculated EPi / SPi - Median EPi / SPi

Appraised Value Sales Price EPi / SPi EPi / SPi-0.9692
689,322 755,000 0.8960 0.0732
689,322 755,000 0.9130 0.0562
734,653 784,500 0.9365 0.0328
794,276 819,500 0.9692 0.0000
829,276 839,999 0.9872 0.0180
939,710 950,000 0.9892 0.0199
947,251 964,999 0.9816 0.9816

Steve worked the formula:

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