Global mean surface temperature is widely used in the climate literature as a measure of the impact of human activity on the climate system. While the concept of a spatial average is simple, the estimation of that average from spatially incomplete data is not. Correlation between nearby map grid cells means that missing data cannot simply be ignored. Estimators that (often implicitly) assume uncorrelated observations can be biased when naively applied to the observed data, and in particular, the commonly used area weighted average is a biased estimator under these circumstances. Some surface temperature products use different forms of infilling or imputation to estimate temperatures for regions distant from the nearest observation, however the impacts of such methods on estimation of the global mean are not necessarily obvious or themselves unbiased. This issue was addressed in the 1970s by Ruvim Kagan, however his work has not been widely adopted, possibly due to its complexity and dependence on subjective choices in estimating the dependence between geographically proximate observations.