On Alexis's credit card statement from last month her outstanding balance was $\$ 539$. During the current billing cycle she made additional purchases of $\$ 30$ on the $10^{\text {th }}$, and $\$ 96$ on the $19^{\text {th }}$. Her payment was received on the $25^{\text {th }}$ for $\$ 100$. Her billing cycle is 30 days. Find her average daily balance.

Step 1 ：Alexis's outstanding balance from last month was $539. During the current billing cycle, she made additional purchases of $30 on the 10th day, and $96 on the 19th day. Her payment of $100 was received on the 25th day. The billing cycle is 30 days.

Step 2 ：The balance for the first 9 days is $539.

Step 3 ：On the 10th day, she made a purchase of $30, so the balance for the next 9 days (from the 10th to the 18th) is $539 + $30 = $569.

Step 4 ：On the 19th day, she made another purchase of $96, so the balance for the next 6 days (from the 19th to the 24th) is $569 + $96 = $665.

Step 5 ：On the 25th day, she made a payment of $100, so the balance for the last 6 days (from the 25th to the 30th) is $665 - $100 = $565.

Step 6 ：The average daily balance is calculated by adding up the balance for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the sum of the balances is $4851 + $5121 + $3990 + $3390 = $17352.

Step 7 ：So, the average daily balance is $17352 divided by 30, which is $578.4.

Step 8 ：\(\boxed{578.4}\) is the average daily balance on Alexis's credit card statement.