Meteorological and oceanographic data from ships of opportunity are the largest contributor to the world's ocean surface data base and thus are extensively used to estimate the change in climatic properties over the world's oceans during the previous hundred and fifty years. The importance of these data for climate change studies underscores the need to fully understand the error associated with averages of these data. The sampling error problem is especially acute for ship data due to the fact that ships are moving platforms and, thus, report observations from constantly varying locations with time. This paper develops a theoretical framework for assessing the averaged sampling error associated with monthly, 1 x 1 latitude-longitude box averaged ship data. It should be noted that time-space distribution of ships within the averaging domain strongly affects the sampling error. This is shown in our derivation. The framework developed here can be used to improve upon existing methods for estimating the sampling error associated with three dimensional box averages of meteorological and oceanographic data obtained from ship records. The framework is complimentary to existing methods of assessing biases and random error due to instrumentation, recording, etc. It is demonstrated mathematically that the uncertainty due to incomplete sampling is primarily a trade off between of the number of observations and their relative locations within the box as well as the inherent time-space correlation structure of the variable of interest. This work differs from other studies in that the three dimensional interdependence of data is taken in account in deriving an expression for the sampling error.