# Update to estimate of population mean based upon new sample

Suppose I sample some phenomenon with a potentially moving mean, let's say height of males on their 18th birthday, and I run this survey every year. Each year I produce a sample mean of height, which will vary (due to limited sample size) even if the population mean remains constant. Suppose aggregate sample mean over the previous three years produces a sample mean of 1.7m, with sample 10,000. If in year 4 I have sample size 50 (ie. small), and sample mean of 1.6m, it's likely that my low sample mean is a result of small sample rather than a shift in population mean.

What would be my best estimate of population mean in year 4, taking advantage of samples collected in previous years? I imagine some adjustment from 1.7m, based upon sample size in year 4 and sample variance but I'm not sure how to approach a solution nor the correct terminology to describe the problem to enable me to find a solution.

Many thanks!

• In which sense is this question deserving the bayesian tag? – Xi'an Sep 2 '18 at 3:58