sizedistribution

Size distribution describes how a population’s sizes are allocated across a range. It expresses the relative frequency of sizes and can be represented as a number-based, volume-based, or cumulative distribution.

In particle size analysis, distributions are summarized by percentile values such as D10, D50, and D90, and by spread metrics like the span or geometric standard deviation. Central tendency is reported as the arithmetic mean or median, or as the geometric mean when data are skewed toward smaller sizes. Many size distributions are roughly log-normal, which influences the choice of metrics and models.

Measurement methods include sieve analysis for coarse particles; laser diffraction or dynamic light scattering for intermediate sizes; sedimentation or centrifugation for finer particles; and microscopy for direct sizing. The choice of method affects the type of distribution obtained (number-based vs. volume-based) and the interpretation of results.

Applications span geology and soil science (grain-size distribution in sediments and soils), materials science and manufacturing (powders, cement, catalysts, pharmaceuticals) for quality control and process optimization, and biology or ecology where size structure of populations is relevant. In industry, size distribution can influence properties such as flow, packing, reactivity, and durability.

Interpretation notes: distributions can be unimodal or multimodal; sample representativeness and measurement biases can affect results. Proper interpretation often requires selecting an appropriate measurement method and a suitable distribution model, such as log-normal, Weibull, or other fitting families.