Based on my experience, public sector HR departments will inform on successful interview outcome quite soon, between one and two weeks. If the vacancy is urgent (such as training course starting soon), they may get back to you on the same day itself if you're selected.

If unsuccessful, HR might delay and waste people's time by informing you of the news 2 to 4 weeks later. However, some ministries will inform you of negative outcome after a few days.

So I guess bottom-line is, really depends on the organization. Its a good HR practice to inform on outcome ASAP, especially if the candidate obviously not selected because fail at the interview stage. It's unproductive to keep people waiting especially if they got other job offers.

Last point: When HR offers a successful candidate only after ONE MONTH (it happens), it really says something about the organization. How can expect people to wait ONE MONTH for your miserable reply, unless the candidate is really desperate.