I want to determine the standard deviation for a set of measurements of a cable profile. However, the cable follows the terrain, and thus using a mean value for the entire cable length does not make any sense.
My current thought is to compute the mean and standard deviation at every point based on the point itself and the two previous and the two next points. Then I can construct a confidence interval for the standard deviation, via the chi-squared distribution, at each of these points.
How can I get a single meaningful overall standard deviation and a confidence interval for it for the entire cable?