This is a question between statistics and calculus. It's from an error propagation problem in a surveying course. We are calculating an elevation based on a starting point, and a couple of different vertical angles. Every measurement includes its own standard deviation. One term, A, is added in the calculation, 1298.88ft. The standard deviation is given as +/- .006. Bear in mind that .006 ft is less than 2mm -- it's tiny. Since a is just a number, the partial derivative of this function with respect to a is 1. The standard deviation of the result of the equation is defined as the square root of the sum of the squares of all the partial derivatives multiplied by their respective standard deviations. So under the radical we see a chain like this: (partialA*sdA)2 + (partialB*sdB)2 + (partialC*sdC)2 -- and then this whole thing is rooted to yield the standard deviation of the equation. The problem is that the standard deviation of A is +/- .006ft That means the actual value of A is somewhere from 1298.874 to 1298.886 ft. This isn't given as .006 per foot, it's .006 total. So I'm not sure what the value of multiplying 1298.88 by .006 is. In fact, it seems that, technically, the larger A gets, the less significant .006 is. Yet I believe I'm being asked to multiply 1298.88 by .006 under the radical. That product is almost 8ft before squaring. Remember, .006ft is only 2mm. So my question is what goes under the radical for this term: (1*.006)2 -- which is .000036 -- or (1298.88*.006)2 -- which is 7.794
This is a question between statistics and calculus. It's from an error propagation problem in a surveying course. We are calculating an elevation based on a starting point, and a couple of different vertical angles. Every measurement includes its own standard deviation.
One term, A, is added in the calculation, 1298.88ft. The standard deviation is given as +/- .006. Bear in mind that .006 ft is less than 2mm -- it's tiny.
Since a is just a number, the partial derivative of this function with respect to a is 1.
The standard deviation of the result of the equation is defined as the square root of the sum of the squares of all the partial derivatives multiplied by their respective standard deviations. So under the radical we see a chain like this:
(partialA*sdA)2 + (partialB*sdB)2 + (partialC*sdC)2
-- and then this whole thing is rooted to yield the standard deviation of the equation.
The problem is that the standard deviation of A is +/- .006ft That means the actual value of A is somewhere from 1298.874 to 1298.886 ft. This isn't given as .006 per foot, it's .006 total. So I'm not sure what the value of multiplying 1298.88 by .006 is.
In fact, it seems that, technically, the larger A gets, the less significant .006 is. Yet I believe I'm being asked to multiply 1298.88 by .006 under the radical. That product is almost 8ft before squaring. Remember, .006ft is only 2mm.
So my question is what goes under the radical for this term: (1*.006)2 -- which is .000036 -- or (1298.88*.006)2 -- which is 7.794
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