Graph Fitting Inquiry

Hello, I am very new user to Igor & IgorExchange. I would like to know if anyone can tell me what curve fitting I can use in the attached graph and how? Is curve fitting really necessary for this graph?
If your advisor tells you to fit some data.... it is always necessary :)

Considering the 'how to', it depends highly on the theory related to the experiment.
Could you give us some idea where the data comes from and what we are looking at?
So far, I see many data points at a single x-value. That might be unusual, it might be not - depending on context. I see some rainbow, but no explanation.

Best,
HJ