RaghavSharma :
Guillaume-RepairItAll :
That's a big discrepancy on ping times. Try to test with only your computer connected directly to the modem wired. Turn off Wi-Fi. See if it remains stable, and goes back to spiking when everything else is on.
Okay. I have a range extender connected directly to my modem via Ethernet, do I unplug that too?
Yes, best to eliminate everything down to the internet connection. This way, if it's your internet line, you would be wasting your time troubleshooting anything else to begin with.
If the problem is not present, and you find yourself with a stable connection for extended time, now you can slowly connect one device at a time back onto the network to see if you could locate where the problem starts.
If you have a bad connection after all on wired, the next thing to verify is your cable. I assume you have a DSL line, so your RJ11 phone cable is the first to check. It should be under 10 feet, and going directly into the phone jack, no phone splitters or ADSL filters should be present. Re-seat the cable make sure it's not broken anywhere. Modem to phone jack direct only. If you're using a coaxial cable modem, than you don't have that step, just have a quick look make sure it's properly connected.
After making sure your connections are fine, if problem persists, contact your ISP tech support, advise them of your test results and that you have already bypassed everything down to the modem, as well as checked the connections. At that point it becomes their responsibility to provide you a minimum QoS.
I should also mention, speed test along side with your ping and tracert testing. Your speedtest results should also help determine any line issues, or if a device is hogging bandwidth.
Here's a scenario example. Say your speeds are not hitting maximum bandwidth on testing while your whole network is on, even though no one is using any device, there is a way to determine the problematic device. Simply disconnect one device at a time, eg phone, computer, from wi-fi or wired, and speed test each time. As soon as you see bandwidth speeds go back up, you just disconnected and identified the problematic device. Could be torrents, virus, malware etc..
Sorry for the lengthy post, hopefully it's helpful to understand some basic network troubleshooting steps that could save you lots of headaches. It's not always fast, but these techniques should help locate your issues with more certainty.