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The relationship between the arithmetic mean and quadratic mean for particle size distribution

  Introduction Particle size distribution data of a material to be collected is very important for the selection and sizing of a dust collector. If a population of particles is represented by a single number (or mean), there can be many different measures of mean sizes (or central tendency): arithmetic, geometric, quadratic, cubic, biquadratic, and harmonic to name just a few, each appropriate to specific uses. The mean particle size is rarely quoted in isolation: it is usually related to some application and used as a single number to represent the full size distribution. It represents the distribution by some property which is vital to the application or process under study; if two size distributions have the same mean, the two materials are likely to behave in the process in the same way. The arithmetic mean The arithmetic mean is the measure of central tendency most widely used in general statistics, and is essential to a few procedures (such as defining a normal prob...