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

[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.

 

[fresh_42]

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.

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.

 

[pixel]

What is the best mathematical way to get the max and min without just picking them by directly observation.

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?