Well, the OP could have simply poked around a (very little) bit and found the answer. A measurement in 1958 put the water depth at the North Pole at 4,087 m (13,410 ft) and a more recent one, in 2007, found 4,261 m (13,980 ft). North Pole. read more
A measurement in 1958 put the water depth at the North Pole at 4,087 m (13,410 ft) and a more recent one, in 2007, found 4,261 m (13,980 ft). North Pole One would also see that the pole happens to coincide with the edge of the Fram Basin, one of the deeper parts of that overall fairly shallow ocean. read more
On 2 August 2007 a Russian scientific expedition Arktika 2007 made the first ever manned descent to the ocean floor at the North Pole, to a depth of 4.3 km (2.7 mi), as part of the research programme in support of Russia's 2001 extended continental shelf claim to a large swathe of the Arctic Ocean floor. read more