In the field of textile research and processing, variability, both of raw material and of measurements, is unavoidable. It is explicitly implied, therefore, that analysis of data should involve an accounting of the variability and should include considerable information concerning the forms of the distribution encountered. In such a presentation, a knowledge of distribution relationships and interrelation ships is of paramount importance. The purpose of this paper is to summarize the relationships between the first few moments of several of the more common types of distributions and to point out a few applications in the analysis of data. Specific problems are in two general categories. First, related distributions, par ticularly those related by a power of the variable, as with number vs. length-biased distributions, will be considered. Second, several problems regarding the sampling of mixed distributions are included. The latter deal with samples from the strata which will comprise the blend or from the blend itself. In each of these situations the effect of single and of bulk samples is treated separately. Finally, some methods of establishing the forms of the distribution are noted for the use of those fortunate enough to be dealing with relatively large numbers of statistics.