Most people are aware of the census records which are available for each decade from 1841 through to the most recently published, that of 1911.
These records are available in summarised book format from places such as the A&NESFHS and the Scottish Genealogical Society or on line at "Scotlands People." (see links)
Family history sites like Ancestry or Find My Past also have a transcription of all or some of these census records but the actual image of the census itself can only be achieved by purchasing it from Scotlands People or calling into a Scottish Registry office.
There are some earlier census records before 1841 for the area included in this study - notably one for 1801 for the parish of Peterhead.
This booklet published by A&NES FHS does contain 6 Andersons, for example a John Anderson living in at Number 8 Quinzie with one other occupant - a woman, possibly his wife.
The booklet also contains an excellent impression of The Town and Parish of Peterhead and a map showing street names - both from around 1801. It can be purchased from the ANESFHS.