Abstract

This study investigates the effectiveness of graphic statistical parameters as descriptors of grain-size distributions. Grain-size distributions which cannot be described adequately using the graphic technique are isolated by comparing the graphic parameters to moment measures calculated for the ungrouped weight frequency data from hypothetical samples consisting of randomly generated "grains" of known size, shape, and density. Differences between graphic and ungrouped mean are insignificant, except for highly skewed distributions. Ungrouped standard deviations generally are larger than their graphic counterparts; the disparity is greatest for medium sorted samples which have long "tails" in the finest or coarsest 5% of the distribution. The respective skewness and kurtosis values are only weakly related, indicating that the graphic measures respond erratically to significant deviations from normality in grain-size distributions. Transformed graphic and ungrouped kurtosis values [kurtosis/(kurtosis + 1)] are more strongly related than the corresponding nontransformed parameters. From these relationships it is concluded that classification schemes of sediment types should make use of graphic parameters only if the range in values of statistical parameters is large enough so that the limitations of the graphic technique do not significantly affect the classification units. It is also established that (a) obtaining data at intervals finer than whole phi is not justified if graphic statistical parameters are to be used, (b) gaussian (probability) interpolations between known points on a cumulative curve and extrapolations beyond the ends of the distribution are required in the calculation of graphic parameters by computers (published computer programs employ linear interpolations and extrapolations), and (c) ungrouped parameters calculated using weight and number frequency are unrelated.

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