I loaded the first page of the Daily Mail Online US Version using several different browsers. I then compared the initial data to load this first page from the Viasat browser, Google Chrome browser, Firefox browser, Opera browser, and the Internet Explorer v11 browser. I left each browser open with no user activity for ten minutes to see if additional data accumulated just because they were left open. The conclusion for this question is that leaving any browser open, even with no user activity, will continue to accumulate data. Therefore, it may be best to close your browser as soon as you are done with it.
Here is what I determined.
These are my results and yours may be different. I am using Windows 7 with an ethernet connection to the router.
My test satisfies me that significant data can be saved by using the Viasat browser instead of the other browsers. (I have no connection with Viasat so I have no hidden agenda).