I write a lot of scripts in Python to analyze and plot experimental data as well as write simple simulations to test how theories fit the data.  The scripts tend to be very procedural; calculate some property, calculate some other property, plot properties, analyze plot...
Rather than just writing a procedure, would there be an benefits of using a Class?  I can bury the actual analysis into functions so I can pass the data to the function and let it do it's thing but the functions are not contained in a Class. 
What sort of drawbacks would a Class over come and what would be the purpose of using a Class if it can be written procedurally?
If this has been posted before my apologies, just point me in that direction.
You don't need to use classes in Python - it doesn't force you to do OOP. If you're more comfortable with the functional style, that's fine. I use classes when I want to model some abstraction which has variations, and I want to model those variations using classes. As the word "class" implies, they're useful mainly when the stuff you are working with falls naturally into various classes. When just manipulating large datasets, I've not found an overarching need to follow an OOP paradigm just for the sake of it.
Class usage in Python