8 years on, this still seems to be a problem, with no satisfactory answers in the StackExchange family.
From this blog post:
ImageMagick's -average operator averages two images at once: the currently considered image, and the result of the previous averaging. It then moves on to the next image.
So rather than every image in the sequence having the same weight, the later images have a higher weight. This doesn't give the result pretty much everybody using this option would intuitively expect. There is also the problem that all the images need to be loaded into memory.
The solution to both problems is a script to call convert recursively, on pairs of images, like this:
#!/bin/bash
i=0
for file in img*jpg; do
echo -n "$file.. "
if [ $i -eq 0 ]; then
cp $file avg.jpg
else
convert $file avg.jpg -fx "(u+$i*v)/$[$i+1]" avg.jpg
fi
i=$[$i+1]
done