how to get the x-value which gives me 50% of area under a curve

[#1]

I have some continuous data and I fit a curve using "Fit Model" and used attributes "Knotted Spline Effect" and 50 knots. Then I save the prediction formula to the table. What I want to do next is to find the fragment size (x-value) which gives me 5%, 10%, 25%, 50%, 75%, 90% and 95% of area. I have 10 samples and so I have 10 very complicated equations.

How do I get the fragment size (x-value) with different area under the curve? I am not familiar with scripts so I prefer learning the mouse clicking way if possible.

Screenshot 2021-09-15 161811.png

[#2]

I use this example to illustrate one approach. I follow the instructions up to step 7. Then from the red triangle menu of the report, I choose "Save Columns" > "Prediction Formula". Now I get a new column, and the formula is the function of the curve. Copy the formula from the column.

Now go to Scripting Index, and find "Integrate" function.

peng_liu_1-1631762883318.png

Now paste the formula and replace the highlighted part, get this:

peng_liu_2-1631762981590.png

Now remove all the colon symbols, by replacing colon by empty string.

peng_liu_3-1631763183428.png

Also replace "x" by "age", my x variable name.

Now decide where the upper limit of the integration (100%), say 80. And the result is 69.783 for 100%.

peng_liu_5-1631763270010.png

Now the task is to find a number to replace 80, and give me 50%: 69.783/2=34.8915. I got 44.228 after maybe a dozen try and error.

peng_liu_6-1631763432932.png

It requires JSL programming, but not much, to get more precise result quickly. Mostly still copy and paste. See the following screenshot.

peng_liu_9-1631764338721.png

The key is to find the value that minimize the squared difference between integral and the target value 34.8919. So I wrap the difference between integral and the target inside of a square, then call minimize function. Check out the function documentation for the syntax. The result for 50% is 44.226900491921.