A huge part if not most of that public sector is education and healthcare. You have a total of 108 people working on those.

 

Well, at least with education, the lifespan of wizards (and the fact that they only spend 7 years in school) would explain this. Since they spend such a smaller fraction of their lives in school than muggles, the percentage of the population needed in education would be much lower.

I'm unsure about healthcare though.

 

The point was mostly that the massive size of Taure's ministry is even more massive when you compare it by industry.

 

Probably because we can't cure and heal almost everything with a bottle or spell and (maybe) an overnight stay. Beds and people for long term treatment are unnecessary if long term treatment itself is unnecessary.

Education is Hogwarts.