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It is a formula which can give you an approximation of the mean (as you're only using mid-points of class intervals for which presumably you don't know how the exact distribution of). As for a physical meaning, it has applications in mechanics too -- you can apply a variation of that formula to find the centre of mass of a system.
Mean can give you value around which the other values of the class are equally distributed.
What is the physical meaning of mean value ?