How to calculate percentile (50th, 16th, etc.) values from grain size distribution. I tried to calculate the percentile (see attachment) by two ways; one is directly from graph method and other from excel software. But the problem is by both methods percentile values are different. I do not understand why is it so.
By which software or formula you mean? Judging from your data sheet, 7.1 looks pretty reasonable as the 50th percentile (which should be the same as the median).
Thanks for the reply.....I am using excel for calculation of percentile (50th, 16th, etc.). Here in this case the phi values lies between 9.13 to 8.97, for 50th percentile.
If you feel brave you should try using R. You could use the quantile(...) function and you can explicitly the probability of the quantile you want to be computed. Besides using excel or R (or other tools), pay attention to the methods used to calculate sample quantiles. look at "Estimating the quantiles of a population" in the wiki page http://en.wikipedia.org/wiki/Quantile.
I'd like to suggest the free software USEPA Pro-ucl for calculation the percentile, it's suitable to evaluate the statistical analysis of environmental matrix
Thanks to all of you .....for your suggestions.......I can easily calculate all those parameters in excel software, but the problem is I am not quite sure in both methods (graphical and calculation using percentile formula) why the values (percentiles- 50th , 16th, etc.) are not same.
I suspect that the reason that you get two different answers is that they are two different approaches and as such will produce different answers. I would just use linear interpolation using the point above and below the 50th percentile. Given the resolution you have it will give you a close approximation. I got a D50 of 7.096022222 microns
Dear Alexander, thanks ...for clarifications .....now I will follow your method.
We do these calculations in our lab quite often. you can easily veryify your result by adding the weight percent column of your data which should add up to 100% over the entire size range. The 50% percentile or d50 does appear to be around 7.14. I have included a Matlab scipt which be modified to use your values and
I found the last two answers very helpful. In case anyone finds it useful, here is a function that will calculate the percentiles based on the ccdall.m posted by Brent. It calculates the percentiles in the same way, but I find functions are easier to adapt to multiple projects.
There are several acceptable methods calculating percentiles.
Do not be too alarmed if your calculator or a friend gives you a value close to but different from what these steps would give.
One very simple way is:
If
P = Total number of candidates
L = Number of candidates whose marks are below yours
Then
Percentile = (L/P)*100 That means if you are the highest in the range, and there are 200,000 candidates and if your marks are same as 7 others then;
Your percentile = (199992/200000)*100 = 99.96
And for more on percentile calculation , Please visit the following link:
http://www.dummies.com/education/math/statistics/how-to-calculate-percentiles-in-statistics/
Happy researching
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