Good day to everyone. I am currently working on my website (http://www.sampleformats.org/) where I am adding formats along with images. I have a question, should I used high definition images (which comes with bigger file size) or compressed images (which comes with small file size)? Both have some merits and demerits base on file usage or size. Please guide me in this regard. Thanks

Why not both? Definition or resolution has nothing to do with compression. It's possible to have a tack sharp, vivid image and still use compression. File size is dependent on the content of the image. Since jpeg uses a lossy compression algorithm the more detail in the image the larger the file. Decide for yourself where the cutoff is between sharpness and compression artifacts.

Alternatively and probably a better solution: include code in your site to detect the user agent, and maintain several versions of your images then serve the one best suited to the user agent environment. Serve higher res to devices with retina displays, smaller images to those on mobile etc. etc.