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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There is no such thing as accuracy when you talk about averages. Make 2 measurements, sum them and divide by 2 and you got average depth, as simple as that. You can add more and more measurements if you want, but there’s diminishing returns, each new measurement will affect the result less and less (10th measurement will affect 10% of the result while 1000th will affect 0.1%), and at some point it becomes so irrelevant – it’s not worth the effort. At the end of the day what it tells you is what depth at any given point is most likely to be, but when you driving your millions of dollars shipt with tens of millions dollar cargo, whould you like it most likely not to run aground or to not run aground?
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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