Table 3, Final Equalization Factors

The department is required to provide an equalization factor for each county that will equalize the level of assessment at the statutory level of 33 1/3 percent of the fair cash value. The level of assessment to be equalized is the mean, or average, of the urban-weighted medians of the three years immediately preceding the assessment year, after adjustment for assessment changes through the current assessment year.

The urban-weighted levels of assessment for the three years involved in the calculation of the equalization factor are shown in Columns 2 through 4. These levels have been adjusted for assessment changes, including those made by any board of review for the current assessment year. Column 5 indicates the mean of the urban-weighted medians for the three years. Column 6 shows the final equalization factor and Column 7 shows the equalized level of assessment.

Formulas for Sales Ratio Studies and Equalization

Sales Ratio=
Prior Year Assessed Value
Current Year Sale Price
X     100%
Coefficient of Dispersion (COD)=
Average Deviation
Median
X     100%
Median Absolute Deviation (MAD)=
Median Deviation
Median of Sales Ratios
X     100%
Coefficient of Concentration (COC)=
Number of Sales Ratios within 10% of the median
Total Number of Sales Ratios
Price-Related Differential (PRD)
          Sales-Based Average Ratio=
Sum of Assessed Values
Sum of Sales Prices
X     100%
          Mean Assessment Ratio=
Sum of the Sales Ratios
Number of Ratios
          Price-Related Differential=
Mean Assessment Ratio
Sales-Based Average Ratio
Equalization Factor=
Desired Level (33.33%)
Prior 3-Year Average Median Level

Examples of Statistical Calculations

Distribution of sales ratios

AssessmentSale priceSales RatioAbsolute deviation from the median
$ 9,000÷$ 45,000=20%15
6,000÷30,000=20%15
9,000÷30,000=30%5
7,500÷25,000=30%5
7,000÷20,000=35%0
7,000÷20,000=35%0
6,000÷15,000=40%5
4,500÷10,000=45%10
7,500÷15,000=50%15
5,000÷10,000=50%35
Total $68,500$220,000355%85

 

Calculations

(derived from above data)

Number of Transfers: 10  
Median:35 + 35
2
=35% 
First Quartile: 30%Third Quartile:45%
Lowest ratio: 20%Highest ratio:50%
Range:(50% - 20%)=30% 

 

Coefficient of Dispersion (COD)

Sum of absolute deviations from the median:85
Average absolute deviation:85 ÷ 10 = 8.5
COD:
Average absolute deviation
Median
= 8.5 ÷ 35% = 24.3%