Math Is Fun Forum

Hi bobbym, I agree that using only the 2 instruments to predict the 90 will be difficult. Especially as under normal circumstances we wouldn't be able to 'temper' the instrument with the 50 percentile data as usually we wouldn't know this. I will look foward to hearing how you get on with this last step. Thank you so much for your help, you have gone way beyond expectations on the amount of time you've spent on this.

Hi bobbym, sounds great! Thanks again

That looks fantastic bobby, thanks so much. When you are happy with the fit/residuals, would
you be able to explain to me what you did to get to this point? Thanks

There are indeed a couple of large departures in the dataset that are a little difficult to decide if they are 'real' or not. Thanks for all your efforts on this, it is much appreciated.

Unfortuntaley I only have the percentile values so I guess the 50th percentile represent the median particle size in microns rather than the mean.

Mainly as to my understanding it's quite useful for summarizing highly skewed data, which I suspect this is.

To my eye the match between the two instruments occurs post-time step 15 where there is a relative increase in the 50% particle size and a slight decrease into the 90%. What is happening here is that the overall particle size range is closer to what the instruments both 'like' to see, hence the similarity in response.

What I was hoping to do was to develop some index that describes the relationship between the particle size and some index of the instrument response. For example, I tries, perhaps naively, plotting the geometric mean of the two instruments vs. just the 50% - the resulting relationship, although weak'ish, showed that as the geometric mean increased, the 50% particle size value dropped. I interpret this as meaning an increasing influence of the 90% but have no idea how you would differentiate between the two instruments e.g. if Ins 1 > Ins 2 or other way round. But I was hoping to be able to something more sophisticated involving the 90% as well!

Hi bobbym, sorry for all this hassle - here is the complete dataset and all should line up (the data goes overnight): time, 50th, 90th, Ins 1, Ins 2

1030,1100,1130,1200,1230,1300,1330,1400,1430,1500,1530,1600,1630,1700,1730,1800,1830,1900,1930,2000,2030,2100,2130,2200,2230,2300,2330,2400,0030,0100,0130,0200,0230,0300,0330,0400,0430,0500,0530,0600,0630,0700,0730,0800,0830,0900,0930

11.351,12.998,12.746,10.233,9.739,13.811,10.571,10.947,10.344,11.019,12.096,13.916,13.919,16.268,16.487,15.389,14.482,14.722,13.56,17.116,10.815,14.5,17.234,18.523,18.121,17.275,19.9,13.05,16.601,18.126,16.717,18.734,19.829,18.677,21.798,16.067,16.643,19.997,20.474,19.652,20.983,18.882,18.712,19.87,18.825,20.268,21.573

51.228,68.811,51.105,34.98,35.117,43.299,46.998,46.477,45.175,54.552,71.006,71.07,93.512,120.178,117.319,102.573,86.405,92.763,73.336,123.759,24.549,77.028,92.082,167.491,158.174,86.375,114.518,108.781,108.259,111.85,84.324,98.898,78.927,96.461,98.442,91.044,75.171,92.825,81.87,101.233,89.004,85.324,76.127,85.562,90.995,103.068,89.413

513,525,556,755,740,856,1139,1218,907,534,536,479,520,249,189,182,168,167,187,265,154,143,152,124,168,127,529,221,215,210,212,174,189,191,193,186,190,193,194,195,195,192,192,194,200,201,207

363,387,409,439,488,519,573,628,737,859,886,733,679,635,576,548,496,495,589,693,632,599,561,529,1557,617,400,225,211,187,169,160,164,156,148,142,139,136,138,140,136,138,147,182,213,223,236

and the remainder of the size data

16.601,18.126,16.717,18.734,19.829,18.677,21.798,16.067,16.643,19.997,20.474,19.652,20.983,18.882,18.712,19.87,18.825,20.268,21.573

108.259,111.85,84.324,98.898,78.927,96.461,98.442,91.044,75.171,92.825,81.87,101.233,89.004,85.324,76.127,85.562,90.995,103.068,89.413

They are most sensitive, generally speaking, to the 5 um to 62 um range so coarse clay to fine silt. Depending on  how the optics are arranged and wavelength, you get varying sensitivity to the really small clays
and to sand.

Hi bobbym
My thinking, which was more than likely incorrect, was that it would make it easier to understand the size mix index if it could be scaled so that 1 represented a large difference between the 50th and 90th values and values closer to 0 represented less of a difference. This was just an arbitrary idea on my part, as, obviously, a non-mathematician.

What I am trying to do is plot/find some sort of relationship between the instrument outputs (I have two that respond in slightly different ways) and the rock size size mix using the 50th and 90th to represent the entire sample. The idea is that if this relationship is reasonable, I can then use just the instrument outputs to roughly determine the rock size mix e.g. proportionally more larger rocks or smaller rocks.

The instruments both respond in slightly different ways especially if there is a lot of larger particles so my thinking was to use these differences to 'predict' changes in the mix of finer and coarser material.  So I guess I have two ratios/relationships that I am trying to compare: one between the 50th and 90th rock sizes and one between the two instruments outputs.