According to RTA specs, it should be painted in White reflective paint, and have narrow keep left signs at each end facing oncoming traffic. Amber reflectors along the sides. And water reliefs every 3m from memory.
The centre lines should have lead on's and off's tapering from atleast 3m from the island.
But this all depends how long ago the medium strip was built.
And it may be a council road? Which council have different specs.
And u are correct, it would have been built to prevent people crossing the road to drive into and out of the childcare centre.