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Users running Avast! Webshield will notice their download speeds running internet ‘Speedtests’ are slow.

From their website:-

Starting from the version 4.6. avast! comes with a new on-access scanning provider – Web Shield.
It is able to monitor and filter all HTTP traffic coming from the Web sites on the Internet. It’s implemented as a HTTP proxy running on your PC.
Connections from your Web browser are redirected to the Web Shield module. Web Shield in turn connects to the requested web server and while downloading the content it scans it for viruses and Trojans. Only the clean data is delivered to the browser, every malware is stopped before it gets saved on your PC.

When running a speedtest Avast! will filter all traffic, this will cause a significant impact on the results.

To get a more accurate result, turn off the Avast! Webshield then run the tests.