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

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1. Jul 20, 2017

### Amany Gouda

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. Jul 20, 2017

### 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
3. Jul 20, 2017

### pixel

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?