I am assuming that you are referring to programs that offer rolling admissions—that is, programs where you can submit an application at any time of the year.
The key words in your question are on average. If you consider all of the applications received by the committee, it will take the committee approximately three months to reach a final decision on a randomly chosen application. However, that is definitely not an exact number—in clear-cut cases, they could reach an answer much sooner. Similarly, applications received during "peak" periods or during the summer—when many faculty are on travel and therefore not as readily available to meet for such decisions—it may take a bit longer.
Part of the reason for this is that several layers of decision are usually involved: first the applications need to be reviewed, and individual members of the admissions committee will have a chance to weigh in. Then, if needed or part of the program's process, interviews will be conducted. After that, the application will still need to be approved by the entire admissions committee, and possibly departmental-level approval will also be required.
If you have not heard anything after three (or better, three and a half) months, then a politely worded email to the admissions office to ask about the status of your application would be appropriate.
On the other hand, if there is a single admissions cycle per year, the decision-making schedule is usually more or less the same each year. Thus, regardless of when you actually submit the forms, notification of the decision comes at the same time for everyone.