Asymmetry and Pearson coefficients

Right skew means a longer right tail; left skew means a longer left tail. A symmetric distribution need not have mean zero. Pearson location-based coefficients are (mean-mode)/SD and 3(mean-median)/SD. They are different summaries and need not equal a third-moment coefficient. The empirical relation mean-mode≈3(mean-median) is only an approximation in suitable distributions. Identify the formula used when comparing results.