In many cases yes, you will be able to reduce it - but it depends on your website design and other factors.

First off - have you optimised the your website photos and graphics? Most Gif's can look just as good with fewer colors, and again most Jpeg's can look just as good with a higher compression level.

You should also look at the coding / HTML of your site to make sure you use relative paths, so that images are not downloaded more than one time.

As a web designer though, you should be doing the above as a matter of course since optimising your website pages makes the visitor experience more enjoyable as your site will load faster for them.