Hi,
If there are a birth and a death within the same quarter, it's very likely to be a baby that died soon after birth that wasn't named... very sad, but not uncommon. It is amazing how much has changed within just over a hundred years--we are shocked by this now, but for our grandparents and great-grandparents, it was part of life. If there's a gap of more than about two years between children, there's likely another child that didn't make it. It doesn't make any of the babies any less precious--my mother tells how her father always remembered one of her ten older siblings, who died within hours of birth--but just the way things were.
Some of the records are for births only, like the one I found today--the name just hadn't been chosen by the time the birth had to be registered. In this case, I believe the child was illegitimate (I'm waiting for the birth certificate to find out), not that this is a reason for not choosing a name, but it may have been a hard time for the family. Or maybe the child was born in a workhouse (as this mother's second child was), and the workhouse authority registered the birth? I must wait (im)patiently to find out!
:-)
Alison