when the committee look at your transcript.. do they care whether say you take statistical methods (easier intro stat class) or mathematical statistics (harder higher level stats).. would they read up the course catalog?

Should I take the easier one to help my GPA if the adcoms doesn't and will not care the difference?..

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You shouldn't think of taking classes in terms of taking "hard" versus "easy" classes. If you do you're approaching education in a completely back-asswards manner. There's no point in taking a class that you don't have the necessary prerequisites for. You have to learn to walk before you can run -- take the lower level statistics and get the foundations of the subject. Once you have the foundations you can always learn the advanced material later, even on your own if you don't have the opportunity to take the class.

Upper division statistics is far more abstract. I doubt it would be particularly useful in physics. You need to know basically two areas of statistics: those that will be useful for experimental methods and those that will be useful in statistical mechanics. Experimental methods (hypothesis testing, etc.) statistics would be taught in a lower division class. You will learn the rest in stat. mech. Take the more useful, lower division class.

No one will care whether or not you took the advanced class -- it won't even be a memorable part of your application. And it's definitely not going to help you unless you get an A, which you might not because you wouldn't have the prerequisites I'm sure.

Upper division statistics is far more abstract. I doubt it would be particularly useful in physics. You need to know basically two areas of statistics: those that will be useful for experimental methods and those that will be useful in statistical mechanics. Experimental methods (hypothesis testing, etc.) statistics would be taught in a lower division class. You will learn the rest in stat. mech. Take the more useful, lower division class.

No one will care whether or not you took the advanced class -- it won't even be a memorable part of your application. And it's definitely not going to help you unless you get an A, which you might not because you wouldn't have the prerequisites I'm sure.