I agree with Mario and disagree Mario Roederer wrote: >Much better would be to calculate the >10th, 25th, 50th (median), 75th, and 90th percentiles of a complex >distribution: at least now you have 5 parameters to the distribution and >therefore a much better chance of accurately describing it (and possibly >discovering underlying phenomena hidden by using only a single value). Using 2 numbers a distribution can however, be completely defined if the underlying distribution is log normal. Particulate systems often have distributions which obey the log-normal distribution. Thus when the distribution is replotted using the logarithm of the parameter, asymmetrical or skewed curves are transformed into a symmetrical "bell shaped curve". In the log normal distribution the mean, median and mode coincide and have identical values. The geometric median and geometric standard deviation completely define the distribution. This is important because you can then apply the statistics derived for the normal or Gaussian distribution to the data. The 10th, 25th etc percentiles give you no extra information IFF the real distribution is lognormally distributed. Incidentally, to put the cat among the pigeons the geometric standard deviation is equal to the 84.1% value divided by the 50% value (which in logs is logX(0.841) - logX(0.5)) These are not my ideas but those of: Stockman, J.D. 1978. What is particles size: The relationship among statistical diameters. In Particle Size Analysis. J.D. Stockman and E.G. Fochtman, editors. Ann Arbor Science, Ann Arbor. If the linear data can not be described by a log normal distribution however then Mario's advice on using the percentiles is certainly useful. Matt Rosinski _______________________________________________________ Matthew Rosinski The University of Queensland Department of Chemical Engineering College Rd St Lucia Q 4072 Australia Ph: (07) 3365 8392/4352 _____________________________________________________
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