Average slope of joined line segments.

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SUMMARY

The discussion focuses on methods for analyzing the average slope of joined line segments. Two primary methods are proposed: calculating the average of individual slopes of each segment and determining the slope of a mean line connecting the first and last points. Additionally, the idea of using a weighted average based on segment lengths or changes in x or y is introduced. The accuracy of these methods is debated, with an emphasis on the context of the problem influencing the choice of method.

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motivehunter
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Hi!

Suppose we are required to analyse the general tendency of a set of joined line segments (to increase or decrease) as shown in the figure, which would be a more accurate method?

1.) Take individual slopes of each line segment and compute the average of all such slopes.



2.) Assume the mean line to be passing through the first and last points and compute the slope of this mean line.


Thanks!
 

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How about a several more ways- take the "weighted" average of the different slopes, weighted by the length of each segment, or by the change in x, or by the change in y?

Which would be more accurate depends upon the particular problem.
 
But can't we assess the accuracy without considering 'problems'? Can't one method be superior to another in all possible ways?
 

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