Given lognormal parameters μ and σ, compute the median (e^μ) and mean (e^{μ+σ²/2}), quantify the skew premium, and show what fraction of the population lies above the mean.
| Constant | Symbol | Value |
|---|---|---|
| Speed of light | c | 2.99792458×10⁸ |
| Planck's constant | h | 6.62607015×10⁻³‴ |
| Boltzmann constant | kʙ | 1.380649×10⁻²³ |
| Avogadro's number | Nₐ | 6.02214076×10²³ |
| Gravitational constant | G | 6.6743×10⁻¹¹ |
| Gas constant | R | 8.31446 |
| Elementary charge | e | 1.602176634×10⁻¹⁹ |
| Electron mass | mₑ | 9.1093837015×10⁻³¹ |
| Proton mass | mₚ | 1.67262192369×10⁻²⁷ |
| Fine-structure constant | α | 7.2973525693×10⁻³ |
Enter the values for the patient or scenario you are assessing. Given lognormal parameters μ and σ, compute the median (e^μ) and mean (e^{μ+σ²/2}), quantify the skew premium, and show what fraction of the population lies above the mean. Use the lognormal mean vs median result to inform your clinical assessment.