when it made sense to average observations. In fact, before the mid-eighteenth
century, they would never combine their own observations with those obtained from
another astronomer. They were fearful that if they combined data that had anything
but very small errors, the process of averaging would multiply rather than reduce the
effect of those errors (Stigler, 1986, p. 4). Taking the mean of multiple observations
became the standard solution only after it had been determined that the mean tended
to stabilize on a particular value as the number of observations increased.