Allow me to add my own data to this. This is from the conversation the Muggle Prime Minister has with "the Other Minister".
'I won't deny that morale is pretty low at the Ministry,' said Fudge. 'What with all that, and then losing Amelia Bones.'
'Amelia Bones. Head of the Department of Magical Law Enforcement. We think He Who Must Not Be Named may have murdered her in person, because she was a very gifted witch and - and all the evidence was that she put up a real fight.'
Fudge cleared his throat and, with an effort, it seemed, stopped spinning his bowler hat.
'But that murder was in the newspapers,' said the Prime Minister, momentarily diverted from his anger. 'Our newspapers. Amelia Bones ... it just said she was a middle-aged woman who lived alone. It was a - a nasty killing, wasn't it? It's had rather a lot of publicity. The police are baffled, you see.'
Fudge sighed. 'Well, of course they are. Killed in a room that was locked from the inside, wasn't she? We, on the other hand, know exactly who did it, not that that gets us any further towards catching him. And then there was Emmeline Vance, maybe you didn't hear about that one -'
'Oh yes I did!' said the Prime Minister. 'It happened just round the corner from here, as a matter of fact. The papers had a field day with it: Breakdown of law and order in the Prime Minister's back yard -'
Harry Potter and the Half-Blood Prince - p.19 - Bloomsbury - Chapter 1, The Other Minister
I think this speaks for itself really. These were wizards murdered by wizards and, clearly, you are quite right. The bodies are found and they do baffle police.
There are surely exceptions to this, though. When Mad-Eye Moody was killed, the Death Eaters "tidied up after themselves" and, obviously, in the cases of wizards who live in Muggle towns and villages and interact somewhat with their neighbours, if they die of old age, presumably it's put down to dying of old age.
As for little kids at Hogwarts, it seems kind of unlikely they would be missed.