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Interpolation offers several advantages, including the ability to estimate values within a range of known data points, which can enhance data analysis and visualization. It is often computationally efficient and can provide smooth transitions between data points. However, its disadvantages include the potential for inaccuracies if the data is not well-behaved or if it contains noise, and it may produce misleading results outside the range of known data (extrapolation). Additionally, the choice of interpolation method can significantly affect the results, necessitating careful selection based on the data characteristics.
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What is Interpolation and why do we need interpolation?
interpolation is basically following a trend. it is needed because one cannot always get enough data to get to where u want to go. GPS units "interpolate" when they loose satellite reception which is why they appear to be tracking in tunnels.
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The advantage is that you will have the same number in each quartile. The disadvantage is that you will not be able to determine the median or mean.
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Interpolation in general is a way to determine intermediate values from a set of coordinates. Linear interpolation would be to fit a single linear function to the entire set of coordinates. Piecewise linear interpolation would then be to determine intermediate values from the set of coordinates by fitting linear functions between each set of coordinates. Connect-the-dots so to speak.
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Advantages over what? For what? Generally linear interpolation is done because one infers that the relationship between points is linear and/or it is the the easiest kind of interpolation. In the absence of data or theory to help you infer the relationship between points the principle of parsimony suggest that use the simplest that gets the job done - linear.
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