Given a sample of data where the samples are taken over irregular intervals, what is the most sensible way of going about calculating the mean and Standard deviation?
Specifically, suppose we are given data to calculate the weekly consumption of coffee in a cafe, but the data is sporadically distributed, showing consumption in anything from one to nine-day intervals. What is the best way of arriving at a reasonable sample mean, and more importantly is there a formal reason for following this approach? Three alternative solutions present themselves to me:
A) Run a mean over each group of intervals separately, then scale it up to 7 and weigh each mean by the number of points contained therein to find a mean across all intervals.
B) Consider only one week intervals etc.
C) Sum the consumption and divide by the total time then multiply by 7.