Mathematics, Statistics, and Quantitative Analysis
Domain 7: Mathematics, Statistics, and Quantitative Analysis
This domain tests the calculations and statistical reasoning used in appraisal: central tendency, dispersion, adjustments, ratios, and income multipliers. You need to choose the measure that fits the data.
Core rules
- Mean is the average; median is the middle value; mode is the most frequent.
- Median is often more reliable when a data set has an outlier or a small sample.
- Range, variance, standard deviation, and coefficient of variation measure dispersion. Coefficient of variation = standard deviation divided by mean, useful for comparing variability across data sets.
- Time adjustments convert a sale price to the effective date using a supported market change rate.
- Gross income multiplier = sale price divided by gross rent.
Worked example
Five comparable sales are $300,000, $310,000, $315,000, $320,000, and $500,000. The mean is $349,000; the median is $315,000. The $500,000 sale is an outlier, so the median better represents the typical sale. The appraiser should investigate the outlier, consider excluding it with explanation, and reconcile toward $315,000 rather than simply averaging all five.
Traps
- Using the mean without checking for outliers.
- Mixing percentages and dollar adjustments in the same grid.
- Applying a time adjustment in the wrong direction.
- Comparing cap rates or multipliers from dissimilar properties.
- Reporting precision beyond what the data support.