Yeah i posed the wrong problem again. Creek always finds a way out
BUT i have another proposal...
First lets state a practical application before parsing it down to mathematics, this is done so the weasel cannot claim
it is an unrealistic or unanswerable or any of his usual tactics.
Civil engunear creek is tasked with building a automated gauge to spit out water level at lake brownwater but he is completely out of his league with this so he asks his buddy goober who is a lectric engunear to help him build the device.
The client wants only the lake level not any info about waves so goober finds a sensor that outputs voltage for the height of the water and mounts it properly. Then he feeds dis voltage into a computer that digitizes the water height with a twelve bit A/D converter which gives numbers between 0 and 4095 which corresponds to a range of -10 feet to plus 10 feet in the water level.
Now goober decides to read in 100 level measurements over a 10 minute period and use these 100 measurements to estimate the lake level.
Now is the best course of action
A Average these 100 readings and use this result
B Some other method
Creeky what would you do with the 100 measurements to give the best estimate.
Say in one batch the lowest reading was 4.73 feet and the highest was 6.35 with a mean of 5.14 feet.
If we can resolve how best to solve this problem we will understand each others position on sig digits.
We still have to define what digits are significant here. It may be sufficiently accurate to say the average is 5.1 feet with a range of 4.7 feet to 6.4 feet. It may also be sufficiently accurate (depending on our purpose) to say the lake level is between 4 and 7 feet with an average of about 5 feet. Of course we could also question weather a 10 minute time period is significant. The lake might be much lower during the August dry season and higher during the April spring flood.
We may also wish to do a normal curve of our 100 measurements to get a minus 1 sigma to plus 1 sigma range too. This would give us an expected range for about 2/3rds of the time. Which may be sufficient in most cases.
For what purpose do we care about the water level in the lake? Presumably we wish to keep the water IN the lake. Presumably we might estimate that if we built a 7 foot retaining wall we could expect to keep the water in the lake almost all the time (based on our short 10 minute time period.)
Are we worried about cattle drinking from the lake? If the water level is under 4.5 feet the cattle maybe unable to drink. Should we plan to pump water into the lake?
I calculate that we would need 11 sixteen inch cement blocks to build a retaining wall at least 7 feet high. (Do remember that a 16 inch cement block is 7 5/8th inches high.) Maybe we should have a foundation too and coping on top. How long will this retaining wall need to be? Will it be supported from the rear?
Or are we building a pool for cooling nuclear power rods near a nuclear power plant in Japan? We may have other thoughts to consider! Will it matter if we get a 30 meter */- 3 meter, tsunami wave after a 9.0 */- 0.5 magnitude undersea earth quake, with a return period of 300 years?