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# Table 1, Assessment Ratios

## Column 1 – Geographic Area (County, township, and multi-township)

This column lists the geographic area to which the ratios apply. Separate township studies are reported if there were 25 or more usable transfers in that township.

## Column 2 – Category

The category shown is “urban,” with the exception of Cook County. For Cook County, the major classes, as defined by the county ordinance, are shown. The Total county median shown in this table is an unweighted median. When sufficient usable sales were available, the urban sales were further separated into “unimproved” and “improved” subcategories. For this purpose, “unimproved” property is defined as a property without a building.

## Column 3 – Adjusted median

The ratio study was conducted using the current year selling price and the prior year assessed value. For example, in the 2007 tables, the 2006 assessments were compared to the 2007 selling price. The ratios are then adjusted according to the percentage changes in assessments made in 2007 by any township or multi-township assessor, CCAO, or board of review. If there was a reassessment in 2007, the adjusted median becomes the level of assessment for that township in 2007. If there were no significant assessment changes in 2007, the median in Column 4 is the 2007 level of assessment.

## Column 4 – Median

The median is the best measure of the average assessment level for a category and a geographic area since it is not unduly sensitive to extreme ratios (as can be the case with mathematical average or mean). The median is the exact midpoint of all individual assessment ratios for a given property and area category. The median is found by ranking the individual assessment ratios in ascending or descending order and counting downward until the middle value is reached. If an even number of ratios is found, the two middle ratios are averaged to calculate the median.

## Column 5 – Coefficient of dispersion (COD)

This statistic provides a measure of the variation of individual assessment ratios around the median. The median indicates the average assessment level but does not provide information about how closely the individual ratios are grouped around it. If the individual ratios are clustered closely around the median, the COD will be low, which implies the assessments are relatively uniform. However, if the individual ratios vary widely from the median, the COD will be high, which indicates that the property was not uniformly assessed and the property tax burden was not fairly distributed among taxpayers in that particular area.

Statistically, the COD expresses the average absolute deviation of the individual ratios from the median ratio as a percentage of that median. The formula for calculating the COD is

Average absolute deviation from the median X 100%
Median

The average absolute deviation from the median is the sum of the differences between each individual ratio and the median ratio (disregarding whether the difference is positive or negative) divided by the total number of ratios.

## Column 6 – Number of Sales

The number shown is the number of “usable” or “arms length” transactions that were included in the study. This figure represents the total number of property transfers used in the analysis.

## Columns 7 and 8 – Quartiles

Just as the median is the ratio that divides the ranking of all individual assessment ratios into two equal parts, quartiles are ratios that divide the ranking into four equal parts. These measures define the distribution in greater detail and indicate any skewness.

## Column 9 – Ratio Range

The range is the difference between the highest and lowest ratios in a given geographic area or category. This measure indicates the absolute variation in the distribution.

## Column 10 – Price-Related Differential (PRD)

In addition to the COD, the intra-area price-related differential can be used as an indicator of assessment uniformity. While the COD measures the general scattering of individual ratios around the median ratio, the intra-area price-related differential measures a pattern of inequity in assessments that has a correlation with the value of the property.

If there is a tendency for the higher-valued properties to exhibit lower assessment ratios than lower-valued properties, the price-related differential will be greater than 1.03. If, on the other hand, higher-valued properties have higher assessment ratios than lower-valued properties, the price-related differential will be less than .98. Differentials greater than 1.03 or less than .98 are both indicative of an inequity in assessment.

The formula for calculating the price-related differential is

Mean assessment ratio
Sales-based average ratio

The mean assessment ratio is the sum of all ratios divided by the number of ratios. The sales-based average ratio is computed by adding all assessed values and sale prices and then dividing the first sum by the second. The intra-area price-related differential, like the COD, is an indicator of a specific type of inequity. It cannot be used to calculate factors that will correct an inequity, nor will it indicate if a particular parcel of property has been assessed fairly. However, it will help locate the source of the inequity so a program can be formulated to correct the inequity.

## Column 11 – 95% Confidence Level

The range in which one can predict with 95 percent confidence the true median assessment level. As the interval widens, the measure of central tendency is less reliable.

## Column 12 – Coefficient of Concentration (COC)

The coefficient of concentration (COC) is a measure of uniformity that measures the percentage of ratios that fall within a given percentage of the median. The percentage from the median used in the department’s calculations is 10. If 50 percent of the ratios fall within 10 percent (plus or minus) of the median, the COC is 50. A higher COC is an indicator of better assessment equity.