UPDATE:
Thank you for your help. You were right!

The problem turned out to be at the connection to the house. At that point, the cable line from the street was fed into two splitters in series to connect 5 or 6 different cables to various cable jacks in our house. The technician said this caused a ton of noise and interference at that point.

The solution was to connect the cable line from the street to only the single cable jack that our modem was connected to. All the other cable lines into the house were left disconnected.

Now my PingPlotter graphs show no packet loss at all!