Particle size, statistics arithmetic mean

For quality control purposes, ceramists are often required to determine if the particle size distribution of one batch of powder is the same or different from another. This determination is difficult when the two batches of powder have similar mean sizes. A statistical method [19] must be used to make this distinction. To determine if two particle size distributions are the same or different. Student s t-test is used by applying the null hypothesis to the two sample means. For normal distributions the f-statistic is defined as tl rati of the difference between the two sample arithmetic means (A and A2) to the standard deviation of the difference in the means [20] ... 

Various molecular weight averages are current in polymer science. We show here that these are simply arithmetic means of molecular weight distributions. It Tiiay be mentioned in passing that the concepts of small particle statistics that are discussed here apply also to other systems, such as soils, emulsions, and carbon black, in which any sample contains a distribution of elements with different sizes. 

Particle size averages This. section describes how to calculate the arithmetic (d) geometric (dg) and harmonic (c/h) means. The derivation of optimal estimates is beyond the scope of this chapter but the interested reader can consult any good statistic book (1.9). The most commonly used averages are the arithmetic averages. The standard formulas for estimating the arithmetic or average diameter and the standard deviation are ... 

Statistically, the particle size distribution can be characterized by three properties mode, median, and mean. The mode is the value that occurs most frequently. It is a value seldom used for describing particle size distribution. The average or arithmetic mean diameter, d, is affected by all values actually observed and thus is influenced greatly by extreme values. The median particle size, is the size that divides the frequency distribution into two equal areas. In practical application, the size distribution of a typical dust is typically skewed to the right, i.e., skewed to the larger particle size. The central tendency of a skewed frequency distribution is more adequately represented by the median rather than by the mean (see Fig. 9). Mathematically, the relationships among the mean, median, and mode diameter can be expressed as... 

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