How do you interpret a DEM? [closed]

Question

I have been asking myself a question for some time. How do GIS experts interpret a DEM (1) ?

In my opinion, there are two ways of interpreting the value of a DEM pixel :

1. Consider that the pixel value corresponds to the value of its centroid
2. Consider that the pixel value is a statistical summary of the measurements made within it

I am aware that membership to one of these two categories depends only on the method of construction of the DEM. For example, a TIN interpolation will assign the estimated value of its centroid to the pixel (case 1), while a statistical method (e.g. mean) corresponds to case 2.

But my question is not which method results to which case, but what is your intuitive interpretation of this kind of data. For you, does an DEM pixel give a summary of the measurements made within it, or does it only give the value of its centroid?

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(1) But the question is valid for any type of raster data.

Answer 1

A DEM is to my understanding usually created from the interpolation from other data sources, typically point elevations and\or contour lines, the pixel being assigned an elevation value. When I use a DEM I think of the pixel representing a constant for all parts of the area a pixel represents. I don't think of it as the value for the centroid of the pixel. But that's just me.