You don't need to write code if you have GDAL installed (if you have QGIS installed that should be the case, but you can install GDAL seperately if you want/need to)
This assumes you want a separate stddev for each image. If you want the stddev across ALL the images, you'll need to do a Raster Merge to combine them into a single raster.
gdalinfo tool with its
-stats option will spit out several summary stats for each band in a raster:-
... snip ...
Band 1 Block=1000x1 Type=Float32, ColorInterp=Undefined
Minimum=11.550, Maximum=26.510, Mean=14.233, StdDev=0.837
If you're using Linux, a short script can be set up to extract the STDDEV for mutiple files. In this case I'm running against hundreds of small ascii grid tiles of Open Lidar Data, and getting a separate stddev for each. You can simply change this to *.tiff; GDAL supports lots of raster formats.
for i in $( ls *.asc); do
gdalinfo -stats $i | grep STDDEV
You should be able to do something similar on Windows if you're using that.