# How to combine dissimilar curves into a single "average"?

With relevance to "functional data analysis", I am looking for some approach which can give an intermediate function among these five different function plots, where this "average function" has the closest distance at each point on the x-axis to each of the five plots.

The plots are shown here for the purpose of the question:

Are there any particular methods one can use?

• Re: "... this "average function" has the closest distance at each point on the x-axis to each of the five plots.", this is given by the function which is simply the pointwise average of your functions. Dec 28, 2022 at 19:02
• @JohnMadden Because of the log scaling of the above figures would you recommend the geometric mean for the "pointwise average"?
– JimB
Dec 28, 2022 at 21:14
• @JimB hahaha got me :) indeed, if you want it to be close on the log scale, we should average in logspace. Dec 28, 2022 at 21:25
• @JohnMadden Just checking to see if I was out of touch. I gave that advice to the OP when that exact same question (but for a potential implementation in Mathematica) was asked at mathematica.stackexchange.com/questions/277880/….
– JimB
Dec 28, 2022 at 21:29