Finding the mode of multiple sample modes I'm running an experiment where I'm collecting samples of different size (numeric data only) and computing the mean, median and mode of each sample. I'm interested in finding out the mode across all samples. I am not sure if I can do this by using the modes for each sample and finding the mode from those modes?
So, I'd like to find
Mode(X)  from Mode(X1), Mode(X2), ..., and Mode(Xn), where X = [X1,X2,…,Xn].
Can I do this by taking the mode from all modes?
 A: One approach to what you're trying to get at is to think of the individual samples as components or subpopulations of a mixture distribution, which covers the overall population. Below is an example of the density functions of two subpopulations or samples of data (dashed lines) that have their own modes. Fitted over them is the overall population set, or global density (solid line), enclosing both.

I wouldn't go so far as to expect that the global density will always have its own single mode, since, for the example shown, it slumps in areas between the subpopulations' modes before growing a hump.
Having a look at the Gaussian mixture model technique might be a step in the right direction to finding a way to quantify the mode of the global density, which likely is some weighted average of the underlying mode probabilities. What's more likely is that mixture distributions will still have multiple modes corresponding to the underlying modes, especially if the gaps between underlying modes are spread far apart.
