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I Max and min values -- Finding them in a data set

  1. Jul 20, 2017 #1
    I have some data collected from experiment and I want to calculate the max and min values for this data.
    Please note that these data not a result of function.
    What is the best mathematical way to get the max and min without just picking them by directly observation.
     
  2. jcsd
  3. Jul 20, 2017 #2

    fresh_42

    Staff: Mentor

    What do you mean by "have" and what by "get"?

    You ask specifically of a mathematical way. So here it is, but you might be disappointed:
    Let ##\mathcal{D}## denote the set of collected data. (This mathematically means: have.)
    Then ##M := \max\{d\,\vert \, d \in \mathcal{D}\}## and ##m := \min\{d\,\vert \, d \in \mathcal{D}\}## denotes the maximum and minimum. (This mathematically means "get").

    Maybe you see the difficulties with your question:
    • Where are the data taken from? ##\mathcal{D} \subseteq## ?
    • How is ##\mathcal{D}## described, i.e. is it a list, a graphic or whatever is it?
    • Are there finitely many of them? ##|\mathcal{D}| < \infty## ?
    • What is the ordering on ##\mathcal{D}## ?
    • Are there eventually algorithms to determine ##M## and ##m## ?
    • Can a order be achieved while reading the data?
    • Is it sufficient to calculate upper and lower bounds for ##M,m## ?
    • Are there uncertainties to the data?
    All these questions might depend on your experiment or might not. As long we don't know any answers to those, the formal definition of ##\mathcal{D}\; , \;M\; , \;m## above is your answer.
     
    Last edited: Jul 20, 2017
  4. Jul 20, 2017 #3
    Do you know how to use Excel? It has min and max functions. Or do you want to write a program and are looking for an algorithm to find the min and max?
     
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