When Thursday Night Football is over, Big Bang and Life in Pieces will be followed by Mom and new comedy Angel From Hell and Elementary. Person of Interest, which did not get a full 22-episode order, will be held for midseason, as are 2 Broke Girls, Mike and Molly and The Odd Couple.
In statistics there are two kinds of means: population mean and sample mean. A population mean is the true mean of the entire population of the data set while a sample mean is the mean of a small sample of the population.
Exactly as Gevorg says, we calculate statistics from the sample to make inferences about the parameters of the distribution. With respect to the idea of a sufficient statistic, informally a sufficient statistic is a complete summary of the information in a sample about some parameter of the distribution. From your example, if we assume that the variance of the Gaussian is known, then the sample mean is a sufficient statistic. If you know the sample mean, you have all the information in the sample about the population mean. If you don't know the variance, then the sample mean and the sample variance are sufficient.