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I find 2.5 interval to twitter has many close servers to users around the world that are not congested are the best to ping too, I understand that other's may like to test using other servers may be best for them.
In the UK we use an Rj11 cable from the master socket to the modem.
So to diagnose until you can prove it is an ISP issue start with the cheapest options first to yourself, replace Rj11 then the Rj45 (Ethernet) and if that does not help then the modem you could ask for a replacement or purchase a better one yourself.
If it still persists it is an ISP broadband or line issue.
Everyone can download PingPlotter ping twitter.com while running a speedtest on a PC or laptop which saturates your line and have the sliders at 100% then on the next test have them at 70% and you will see the results for your own line.
Test using preemptive then with reactive to find the lowest jitter between the two.