All methods of measuring the integrated properties of cloud, rain, or hail populations such as the water content, precipitation rate, kinetic energy, or radar reflectivity are subject to statistical sampling errors due to the Poisson distributed fluctuations of the number of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. This work generalizes and extends that of Joss and Waldvogel (1969) by providing a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X (D) =cDn for any particle size distribution where D is the particle diameter. In addition, for the case of exponential size spectra we derive general expressions for the FSD of all integral parameters for sampling devices of constant volume or for (area¿time) devices in which sampling volume is a function of particle fall speed. We present a set of universal curves applicable to the exponential size distribution which permits the estimation of the FSD of any such parameters from n=0, which corresponds to the measurement of total number concentration, to n=6, which corresponds to the radar reflectivity factor. Equations and curves are also provided to permit corrections for finite upper limits to the size spectrum and, in the case of rain, for a realistic fall speed law. Examples are included to illustrate the magnitude of the expected FSD for a variety of rain and hailfall parameters with sampling instruments now in use. A comparison is made with observed rainfall data to illustrate the methods presented in this paper and some of the difficulties in distinguishing fluctuations of physical and statistical origin.