Can I recover app data after the phone has been Factory Reset? Without remembering application data, I reset my Galaxy S3 to factory state. Now, I lost data for one expense manager app. Is there any way to recover the data?
NO. Unless you perform a backup before, you lose all app data during a Factory Reset.

Factory reset
A factory reset or master reset is a full restore of an electronic device to its factory settings. Such electronic devices include handheld computers such as PDAs and mobile phones. It entails deleting all information stored in the device. This is essentially the same as reformatting a hard drive. A factory reset may become necessary from time to time on a device which is no longer working. It should be used with caution, as it destroys all data stored in the unit. Many problems with a hand held electronic device such as freezing can be resolved by performing a factory reset or hard reset.

Wikipedia Article