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I'm currently creating a table containing values for a number of variables, many of which actually are the mean values. To indicate that those are the mean values, I use the bar on the corresponding variable in the header (e.g. $\bar{x}$). Maybe this is not the standard way in maths, but it's common in my (physics) community.

Now I also have a column where I would like to give a range for the corresponding variable, but I can't think of a good way to indicate this, so people can intuitively understand it. Of course I can always just some "arbitrary" indicator (e.g. $\tilde{x}$, or $\hat{x}$) and explain what I mean by that in the notes. In addtion, I of course also need to indicate the range in the value cells themselves, e.g. $a-b$, $[a, b]$, or $a<x<b$ (of which I actually prefer the first, I know, not very mathy).

I was just wondering if there is something more intuitive.

The only other idea I could think of is the make two colums, one with $x_\text{min}$ and one with $x_\text{max}$ (or $\text{min}(x)$/$\text{max}(x)$).

Example showcasing the different approaches (note that in the actual table I wouldn't write mean/range of $x$ in the header in addition to the symbol):

Cases mean of $x$: $\bar{x}$ range of $x$: ?? $x_\text{min}$ or $\text{min}(x)$ $x_\text{max}$ or $\text{max}(x)$
First 1 $0-2$ 0 2
Second 2 $[-1, 4]$ -1 4
Third 3 $1 < x < 6$ 1 6

Apologies if this is not the correct community. I found this post and thus thought to give it a try here.

mapf
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    I don't understand the sentence Now I also have a column where I would like to give a range for the corresponding variable. Can you elaborate? – mathcounterexamples.net Jul 05 '22 at 15:21
  • Hi, thanks for the question. I've added an example for clarification. – mapf Jul 05 '22 at 15:35
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    $\bar x$ is indeed the most common notation in mathematics for the mean of a statistical variable $x$. All three range specifications are commonly used, so there should be no problem there, either, with you choosing your favorite. $a - b$ might be confused with subtraction, but it is still a fairly common notation, and I doubt in the context that more than a rare few would have any trouble with it at all. – Paul Sinclair Jul 05 '22 at 16:19
  • Hi @PaulSinclair, thank you! The option with the minus-sign was actually supposed to represent an en-dash, but the latex syntax (--) is not correctly interpreted here, so I went with $-$ instead. I guess that's what I will stick with then. – mapf Jul 05 '22 at 16:25
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    FWIW, an en-dash is gotten with $0$--$2$. (The "--" construct must be in paragraph mode, not math mode.) <> If we're nitpicking, a range to me is a noun, so interval notation is appropriate, while inequality notation, a condition specifying bounds, is a small stretch. Separately, it's worth considering whether reporting redundant information (range, as well as min/max values) is clarifying. Finally, this seems not to be your situation, but an interval $[x_0-r, x_0+r]$ centered at $x_0$ might usefully be denoted "$x_0\pm r$." – Andrew D. Hwang Jul 05 '22 at 17:23
  • Thank you, @AndrewD.Hwang, I certainly appreciate your nitpicking! I'm not very familiar with math terminology however. Could you explain why the word range being a noun is relevant? That sounds interesting. I also like the inequality notation the least, since it uses the most space, characters, and ink, and just doesn't look good if repeated like that (especially because you need to use the variable symbol every time). Also, my values are actually measurements, so I made a mistake and it should have been $a \le x \le b$. – mapf Jul 05 '22 at 17:52

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