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I have a data set in excel of almost 6000 entries (quantitative and continuous => P(X=x)=0, I mean the possible values for my continuous random variable X are uncountably many). Each point will represent a particle with a determined surface area.

     A total of 5168 enclaves with a large 
     variability of size (area) ranging
     from 2.00x10^-3 to 7,98x10^2 mm2.
     With an increment=0,0002 , calculated in excel by =1/COUNT(A:A) (A=column with the values of surface area).

I need to determine the Fragment Size Distribution (FSD), and present it as Cumulative Frequencies, on log-log plots, where the slope of the linear point arrangement is the value I need to get (Fractal Dimension of the FSD).

Since I'm a beginner in statistics, and I have read that it's not necessary (nor recommended?) to bin continuous data, I wonder if there any good way to do this, without binning my data? I have tried the following:

  • I tried calculating the Cumulative frequencies by binning (in an empirical way), with different bin width and the value of my slope changed with every new value.
  • I applied Freedman-Diaconis Rule trying to “bin” my data: enter image description here Applying log scale for the y-axis: enter image description here Freedman-Diaconis Rule: Gives high number of bins, distribution positively skewed, but the distribution does not show much information, since many of the latest classes have no population.

  • I plotted the Cumulative Normal Distribution (on excel), as well as the CDF (Cumulative DIstribution Function), then I applied log-log, but I didn't get a linear point arrangement. enter image description here enter image description here

Is there a problem with my data? I tried it again using just part of the data, but it didn't work either. If I don't bin my data what is the correct way to proceed with my data set to determine the Fragment Size Distribution (FSD), as Cumulative Frequencies?

Probably this hasn't much sense since my statistical knowledge is very basic, but I really hope you could understand and could help me out here.

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