system
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“msn explorer” combines a browser with “Live” features (hotmail, live messanger…). This means that there “must” be some bandwith constantly used, even if you are not directly using it (you are not currently chatting, but the system needs to be active anyway).
Avast “may” be checking the data being transferred, but Avast itself is not generating the transfer.
BTW, to test your bandwith with speedtest.net, you should “exit” any “live” service, any chat method, any social communications, any browser, any FTP, any “toolbar”… The only active connection should be one simple plain web browser window with the speedtest.net site on one only tab. Please note that “exit” is not the same as “minimize” nor “close”.