I'm having a hard time understanding the use of MLE. I understand what it does, it is intended to give the best parameters for a particular model to represent a population.
My question is, is MLE necessary for getting the best model parameters? Isn't if possible to do this calculation manually?
For example, if I want to calculate the best parameters of a Gaussian Distribution for the following population...
I would need the mean and standard deviation, I can calculate those myself, they come out to be 49.8 and 11.37 respectively. So my question is, what benefit does MLE give over the standard way of computing these parameters?
I apologize if this question is naive, I have just been introduced to MLE and my background is not in statistics so I am trying to wrap my head around this.