Why would you want to calculate average shareholder equity?
Average shareholder equity is a common baseline for measuring a company's returns over time. Using average shareholder equity makes particular sense if a company's shareholder equity changed from one period to another. That number can change because of retained earnings, new capital issues, share buybacks, or even dividends.
For example, a company may have shareholder equity of $1 million as of the first quarter and then issue new shares during the second quarter, raising shareholder equity to $1.5 million. Their average shareholder equity then for the first and second quarters is $1.25 million.