The average on your card is maintained on a target year basis, with no carryover from the prior year. Started over again September 1st. All targets hit divided bt all targets shot in the target year is the correct method. Don't listen to anyone that tells you to use some shorter time frame - like last 1,000 targets etc.
As stated your average (actually percent broken) begins new every target year.
870 is correct.
You calculate it by adding the cumulative total targets broken for the entire current target YEAR (not the last shoot unless you're just interested in seeing how you did for that shoot); and divide this sum by the total shot at for the year.
Total broken/total shot= your "average", or more accurately the percent of targets broken.
Look at TC.com's home page under Fun Stuff and you will find an Excel spreadsheet calculator that does it automatically. Copy it and save it to your PC. It's an excellent tool for keeping track on how you're doing and for updating your ATA Average Card.