What is the average price of a good battery back up sump pump system installed?

Hard to price on a universal basis. We don't know what quality battery, difficulty etc. Get 3 estimates from trusted plumbers.

How much does a steak cost on average? A Car? Same reason nobody can answer that, can answer your question either. Specifics are needed.

Why would you need a battery back-up for a sump pump? Do you have a sump hole? Is the flow so heavy that a power outage would overflow into the basement? More facts please.

Wayne 1/3 HP - 12 Volt Battery Backup Sump Pump System-ESP25 at The Home Depot

You would also need to buy a battery for it. Worked for my usage. My basement (not really a basement but more of a dirt and stone 10x10 room that holds the furnace and water heater) takes on water pretty quickly during the wet season. I have lost power before for 6 hours and had enough in the basement to start flooding the furnace as it is only 8 inches above the ground. I have a generator to run a secondary pump if we lose power but the battery pump is in case I am not around and it happens.