There are definitely people your age who I've seen on the forums get into programs and worked with on set! It all depends on the individual.
But in terms of statistics and anecdotal observations....It seems like the average age for MFA programs is in the late 20s or early 30s. Not only for film but across the board based on published statistics available on Petersons or US News. This seems pretty consistent for other types of graduate school also. Admissions often want to see someone with 'life experience'. The same seems to go for film programs. I don't think your age is a good or bad thing as long as you demonstrate a dedication, work ethic, and maturity/professionalism towards your studies and film career. Industry-wise, while the 'face' of film is often young, the average entry level but full time crew member is in their mid to late 20s or older (really that goes for strong set PAs, costumers, electrics etc). I think that has a lot to do with the maturity of dealing with people, long hours, professionalism, patience, etc etc, but typically these positions require a lot of energy so the age part needs a balance. Film hiring revolves around the same things all professional careers would be looking for in good workers. (I work full time in the industry for over 5 years now myself, starting as a PA and now as an AD, this is based on my personal experiences on known movies, tv shows, and commercials. As well as my own hiring practices).