- Empirical Rule (Approximation): Think of this as a quick-and-dirty rule for the boards. It’s easy to remember:
- ±1 SD ≈ 68% of data (Actual Z-score for 68% CI is ~1.0)
- ±2 SD ≈ 95% of data
- ±3 SD ≈ 99.7% of data
- Z-score for Confidence Intervals (Precision): This provides the exact value needed for formal statistical calculation. For a given CI, you find the Z-score that leaves the remaining percentage split equally in the two tails.
- 95% CI: Requires the central 95% of the data. The remaining 5% is split into two 2.5% tails. The Z-score corresponding to this is 1.96.
- 99% CI: Requires the central 99%. The remaining 1% is split into two 0.5% tails. The Z-score for this is 2.58.