Initially, the system filters the data and calculates mean and standard deviation values for the selected measurables. The mean is the average, and the standard deviation measures how "spread out" the data are. For example, the set of numbers (2, 4, 6) has a lower standard deviation than (2, 6, 10). The combination of these numbers allows statisticians to introduce a standardized unit called a z-score, which measures how far above or below the average a given measurement is.
Z-Score = ((Metric - Metric Average) / Standard Deviation of Metric))
We then combine these z-scores across multiple metrics into an index score. But before we do that, we apply weights to each z-score. This allows us to weight certain metrics more or less heavily in creating the index.
Weighted Z-Score = ((Metric - Metric Average) / Standard Deviation of Metric) * Weight
The system multiplies the Z-scores by their assigned weights and then aggregates these weighted Z-scores into a composite score.