Your neighbour is stealing power. 15kwh/day means you are permanently using 600 Watts. Do you have a stationary (desktop) computer? Or do you underestimate heating. You can burn through your whole years budget easily in less than two month. What about the oven, I mean do you bake?
Sounds about right. My house, at idle, uses 300w last time I measured it, probably more now. Most of that would be electronics. A rack in the garage with a 24 port PoE switch powering a couple of APs, and a router, a NAS, a handful of small devices, plus whatever drain is used by the various laptops and iMac at sleep, and the clocks on the various appliances, the small aquarium pump on the cat fountain.
The appliances, as I mentioned, are all gas, but still a clothes dryer and a washing machine consume some electricity, as does the pump on my furnace, as do ceiling fans in use when necessary.
And of course, the devices that cycle on and off all the time; the refrigerator, instant hot tap under the sink.
And then there's the actual electricity we consume during the times we're home to do things like light the house, watch television or use computers, listen to music, etc. It is quite easy to use 2000-2500w when home and active in the evenings.
He did say gas appliances which I assume would include the oven and might include a dryer. Presumably not the refrigerator though (there are propane refrigerators but you wouldn't normally get one if you have electricity). I probably draw 400-500 watts even if I'm traveling.
A decent refrigerator should consume less than a kWh per day, perhaps 1.5 kWh/day for refrigerator + standalone freezer - this is something that has changed over the last couple decades, at least in the EU there has been a strong push towards more efficient appliances and refrigerators consume much less power than older models.
This does not make it more likely that someone is stealing their electricity than they have a refrigerator and/or freezer making up the rest of their unspoken for electrical bill.
