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A star count is, in effect, an survey (or analysis of existing survey data) counting stars according to some criteria. A motivation for such bookkeeping has been to determine the density of stars, through classifying them by apparent magnitude and making adjustments to accommodate biases that affect the counts, such as the Eddington bias and Malmquist bias. Another motivation is determining the birthrates and lifetimes of different spectral classes.
Analogous counting and analysis is used for other astronomical phenomena, e.g., galaxies, supernovae, and extra-solar planets. Counts of the former two are considered revealing regarding current ideas in cosmology.