Laser diffraction instruments should allow users this flexibility.Īn additional approach to describing distribution width is to normalize the standard deviation through division by the mean. In rare situations the span equation may be defined using other values such as Dv0.8 and Dv0.2. One of the common values used for laser diffraction results is the span, with the strict definition shown in the equation below (2):įigure 4: Three x-axis values D10, D50, and D90 ![]() Once “model independent” algorithms were introduced many particle scientists began using different calculations to describe distribution width. Although occasionally cited, the use of standard deviation declined when hardware and software advanced beyond assuming normal or Rosin-Rammler distributions. As shown in Figure 3, 68.27% of the total population lies within +/- 1 St Dev, and 95.45% lies within +/- 2 St Dev. The standard deviation (St Dev.) is the preferred value in our field of study. The most common calculations are standard deviation and variance. The field of statistics provides several calculations to describe the width of distributions, and these calculations are sometimes used in the field of particle characterization. Experienced scientists typically shun using a single number answer to the question “What size are those particles?”, and prefer to include a way to define the width. Most instruments are used to measure the particle size distribution, implying an interest in the width or breadth of the distribution. The mean value is flanked by 1 and 2 standard deviation points. For the denominator take the geometric D i to the third power multiplied by the percent in that channel, summed over all channels.įigure 3: A normal distribution. For the numerator take the geometric D i to the fourth power multiplied by the percent in that channel, summed over all channels. The D i value for each channel is the geometric mean, the square root of upper x lower diameters. The best way to think about this calculation is to think of a histogram table showing the upper and lower limits of n size channels along with the percent within this channel. The equation for defining the volume mean is shown below. ![]() Laser diffraction results are reported on a volume basis, so the volume mean can be used to define the central point although the median is more frequently used than the mean when using this technique. 3) for an explanation of number, surface, and volume distributions. There are multiple definitions for mean because the mean value is associated with the basis of the distribution calculation (number, surface, volume). The various mean calculations are defined in several standard documents (ref.1,2). ![]() Mean is a calculated value similar to the concept of average. Figure 1: Symmetric distribution where mean=median=mode
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