Yes. But carpet and underlay helps a lot.
The other thing is the plaster on the ceiling below. I formerly had a house with thick, heavy lime plaster. When some of it had to come down, I was startled by how much noise came through the uncarpeted bathroom floor.
A modern house usually has a single layer of plasterboard with a thin plaster skim, which is not as good. If you ever need to have ceilings skimmed, for example if you want to cover artex, and you have a particular noise problem, consider having an extra layer of plasterboard added first.
Lastly, any holes or gaps in ceiling will allow noise through. It gets through the weakest spots. There are usually gaps hidden by the lighting roses, and around pipes, and sometimes above cupboards, boilers etc where the plasterer's work was unseen. There are even people who like multiple holes in their ceilings for lamps to poke through. As well as noise, these holes allow odours, draughts, and even smoke or fire, to pass through the ceiling barrier. You can often fill them with expanding foam (get the pink, fire-resistant grade)
If you ever have to take the floor up, fill all possible holes and gaps. There will usually be a gap under the skirting, and gaps in the mortar and brickwork that are out of sight.
You can also put mineral wool quilt between the joists, especially packed tightly round the edges of the room where most draughts get in. Ordinary loft insulation makes a slight difference, you can buy dense builders batts which are better (the extra mass deadens sound more). Don't put it under a bathroom floor where it may get wet.
Pic: A recent floor. You can't see the pink foam applied to the joint between the walls and the upper surface of the ceiling, and all pipe or cable gaps.
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