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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Averaging
From: Alexandre Eremenko
Date: 2004 Oct 19, 00:01 -0500
From: Alexandre Eremenko
Date: 2004 Oct 19, 00:01 -0500
I think the question whether the averaging of observations (before reduction) is justified, or under what conditions is it justified is important and worth further discussion. In his last message on the topic, Herbert Prinz challenged this practice referring to non-linearity of altitude change. I agree that under some circumstances this non-linearity may introduce substantial error, however I feel that these circumstances should be rare. I am sure that Herbert's statement that: "manual averaging is a thing of the past" is an exaggerration. Many modern manuals do recommend such averaging, and I am sure that people who tried it know that it usually increases presision, without any substantial increase in volume of computations (which will happen if we reduce each sight separately). On other aspects of averaging recently discussed. 1. There is NO mathematical reasons for averaging even or odd number of observations. (This I can say as a mathematician who teaches statistics classes:-) If there are any other (non-mathematical) reasons, I don't know, and it is hard to imagine what these other reasons could be. 2. Median (middle value) is indeed frequently used in statistics (like median income, median housing price, or median score on an exam). But this has nothing to do with the problem we discuss: of reducing random errors in observations. The situations where using median is recommended are DIFFERENT. Median can be computed independently of whether the volume of the sample is even or odd. In the even case they take the average of the two middle values. But I repeat, median is not the best thing to do to reduce random errors in a series of measurements. I can give specific examples which explain why sometimes median is used but this will be definitely out of scope of this list. To reduce random independent errors in a measurement of a quantity that changes linearly (or does not change at all), average is the proper thing to compute. Alex.