For example, I have made a TIN from a contour shapefile around my sites (Figure 1 edited with river shapefile) and then converted that to a Raster shapefile (Figure 2). The problem is I can't find how to calculate this within specific buffers.

I would like to be able to calculate a 'Terrain Ruggedness' index for each one of my sites in my study area and found a couple different suggestions, but I think calculating the standard deviation of elevation would give me useful values. I'm fairly new to GIS and I haven't been able to find much on this specific topic in the ESRI community. I've already posted this so I apologize for any confusion, but I accidentally marked the question as 'Assumed Answered' and it's not allowing me to change that or erase my post, so here it is again.