Parametric probability distributions can be fit to a dataset by equating sample L moments to those Of the fitted distribution. This study examines the mean and mean squared departures of sample L moments of monthly precipitation data from large sample values as sample size increases. Mean departures decrease as the sample size increases with values near zero generally occurring with about 30 to 40 or more observations for the central tendency measure, about 40 to 50 or more for the dispersion measure, and about 60 or 70 for the skewness and kurtosis measures. It was also found that the root-mean-square departures appear to decrease linearly with the square root of the sample size. The results are intended to provide guidance for determining sample sizes when applying at-site L moments to monthly precipitation data. Abstract Parametric probability distributions can be fit to a dataset by equating sample L moments to those Of the fitted distribution. This study examines the mean and mean squared departures of sample L moments of monthly precipitation data from large sample values as sample size increases. Mean departures decrease as the sample size increases with values near zero generally occurring with about 30 to 40 or more observations for the central tendency measure, about 40 to 50 or more for the dispersion measure, and about 60 or 70 for the skewness and kurtosis measures. It was also found that the root-mean-square departures appear to decrease linearly with the square root of the sample size. The results are intended to provide guidance for determining sample sizes when applying at-site L moments to monthly precipitation data.