The average depth of the sea or a lake can be measured with the accuracy of one meter. How do they achieve such accuracy? Do they send sonar like signals on every square kilometer of the lake and then average the results?
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they do send sonar signals and average.
They do not do it on every square kilometer because that would take forever and cost a ton. They run a sonar while a ship travels, criss-cross the ocean along several different routes, then make assumptions about depths of the remaining areas.
As for precision, this is the excellent point. The averaging function in computer will report result with whichever number of digits you choose. The actual accuracy must be computed using statistical formulas for standard error, but that is a lot more work, so many people skip it.
A sonar measurement in a single spot can be accurate to a meter, and it can be made more accurate by taking several measurement in the same spot, and averaging them. Sonars are used to find shipwrecks on seafloor, like a mile down.
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