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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
| Assessment | Sale price | Sales Ratio | Absolute 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 | $220,000 | 355% | 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% |