Changing the DNS may or may not improve your browsing experience but it won't have any effect on speedtest results. Any variation will be pure chance.
My own connection is normally fine but yesterday evening it all when to pot with a terrible looking TBB ping chart and a drop in down from 50 to ~30 and upstream sub 2 when it's normally ~ 4.5. On cable **** happens and it can happen very quickly it seems. I'm hoping mine will go back to normal and this was just a new 100Mbps customer downloading the internet.
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