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I realize there is probably a forum on here already that addresses this, but I am probably missing what term(s) to search for.

The situation is, we have an online form that allows users to put in 4 whole numbers. The minimum the form will accept is 70, and the maximum is 300. Sometimes, numbers outside this range are actually OK if the numbers relate to each other properly. For instance, a good set is:

  1. 70
  2. 150
  3. 95
  4. 80

An acceptable set, outside those limits on the high end, is:

  1. 122
  2. 305
  3. 215
  4. 150

An acceptable set on the low end might be:

  1. 58
  2. 100
  3. 75
  4. 60

An unacceptable set would be:

  1. 17
  2. 200
  3. 100
  4. 85

Above, the first number is FAR too low, and the gap between 1 & 2 is also too large.

Another unacceptable set would be:

  1. 95
  2. 60
  3. 500
  4. 88

The pattern we're looking for is:

  1. "Acceptable" range which is really more like 45-130 for point 1. First point can't be above 130, this actually IS an inflexible requirement. Could realistically be much lower than 70. Anything lower than 45 would be suspect her and a more realistic cutoff.
  2. Should be higher than point 1. Above 300 is suspect, but might be fine if point 1 is relatively high.
  3. Should be lower than point 2
  4. Probably Lower than point 3, but could be the same or very slightly higher and still be considered acceptable.

So, a curve of sorts. I'm looking for some ideas of formulas to use to look at our ACTUAL accepted data to make a better form (with more realistic limits), and maybe even use a formula to evaluate the results relative to one another instead of just using high and low cutoffs.

It's been probably a decade since I took a math class so I'm really starting from scratch here, even just a nudge in the right direction would be great.

  • What is the name for this type of "curve evaluation" as I'm calling it?
  • What should I research further to find out what's possible here?

I'm thinking either calculus (because curves) or statistics, or a combination of the two, because I want to use existing data to inform what would probably be some kind of calculus formula that I'd use to evaluate incoming data sets for validity.

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closed as primarily opinion-based by BruceET, Saad, Mohammad Riazi-Kermani, Xander Henderson, Namaste Mar 7 '18 at 1:07

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ As you are talking about relating properly, so you definitely need to use fractions, i.e. $\dfrac{17}{200}=0.085 < r$ is lower than a cutoff ratio so unacceptable, but $\dfrac{122}{305}=0.4>r$ is not lower than the cutoff ratio and is acceptable. For instance, you can set the cutoff ratio to $r=0.3$ or so... . $\endgroup$ – Mehrdad Zandigohar Mar 6 '18 at 19:57
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    $\begingroup$ This is an interesting empirical problem whose solution might involve some easy mathematics - but the only way to know is to thoroughly explore the data you have, particularly the cases you accept even though they are beyond your stated m criteria. You could look at ratios (as suggested) or clustering. You could try to explain in words (for yourself) why some exceptions are OK an others not. Look at the close calls. But I don't think anyone here can suggest possible rules without looking a lot at your actual data. $\endgroup$ – Ethan Bolker Mar 6 '18 at 21:10
  • $\begingroup$ Source of data, reasons for collecting data, tolerances for departure from rules, objectives of data analysis are all unclear or unspecified. Any answer from here would have to be an uninformed opinion or unwarranted guess. $\endgroup$ – BruceET Mar 6 '18 at 23:00