how deep is the most-deep point of the ocean?

The Challenger Deep is the deepest surveyed point in the oceans. It lies in the Mariana Islands group at the southern end of the Mariana Trench. The closest land is Fais Island, one of the outer islands of Yap, 289 km southwest and Guam 306 km to the northeast. The point is named after the British Royal Navy survey ship HMS Challenger, which first discovered the trench in 1872.

Depth
The maximum surveyed depth of the Challenger Deep is 10,923 meters (35,838 feet) or 6.7875 miles. (National Geographic puts the depth at 11,034 meters (36,201 feet) below sea level.) The pressure at this depth is approximately 1095 times that at the surface, or over 16,000 pounds per square inch (110 MPa).

The HMS Challenger Expedition (December 1872 - May 1876) first sounded the depths now known as the Challenger Deep. This first sounding was made on 23 March, 1875 at station 225. The reported depth was 4475 fathoms (8,184 m, 26,850 ft), based on 2 separate soundings.

A 1912 book, The Depths of the Ocean by Sir John Murray, records the depth of the Challenger Deep as 9,635.9472 meters (31,614 feet). Sir John was one of the Expedition scientists, a young man at the time. Page 131 of Murray's book refers to the Challenger Deep. All of the reports of the original Challenger expedition can be viewed on the web at the Challenger Library.

In 1951, about 75 years after its original discovery, the entire Mariana Trench was surveyed by the Royal Navy vessel HMS Challenger, named after the original expedition ship. During this survey, the deepest part of the trench was recorded using echo sounding, a much more precise and vastly easier way to measure depth than the sounding equipment and drag lines used in the original expedition. HMS Challenger measured a depth of 5,960 fathoms (10,900 m, 35,760 ft) at 11°19′N, 142°15′E.

On 23 January 1960, the Swiss-built Bathyscaphe Trieste, acquired by the U.S. Navy, descended to the ocean floor in the trench manned by Jacques Piccard (who co-designed the submersible along with his father, Auguste Piccard) and USN Lieutenant Don Walsh. The descent took almost five hours and the two men spent barely twenty minutes on the ocean floor before undertaking the three-hour-and-fifteen-minute ascent. They measured the depth as 10,916 metres (35,813 feet). At the ocean floor they observed small sole and flounder and noted that the floor consisted of diatomaceous ooze.

In 1984, a Japanese survey vessel using a narrow, multi-beam echo sounder took a measurement of 10,924 meters (35,838 feet).

On 24 March, 1995 the Japanese robotic deep-sea probe Kaiko broke the depth record for unmanned probes when it reached close to the surveyed bottom of the Challenger Deep. Created by the Japan Marine Science and Technology Center (JAMSTEC) it was one of few unmanned deep-sea probes in operation that could dive deeper than 6,000 metres (19,680 feet). Its recorded depth of 10,911 m (35,797 ft) for the Challenger Deep is believed to be the most accurate measurement taken yet. Kaiko also collected a sediment core from the bottom of the deep.