The roles of sample mean and sample variance in the statistical landscape

Sample mean and sample variance can be taken as a “genetic code” of data. Information on average and spread of the sample data is provided by these measures. But these values play a significant role in a wider perspective in inferential statistics. In testing of hypothesis, the hypotheses of population are tested on the basis of test statistics based on these measures. Intervals within which the unknown population parameter lies are also built with these measures. These intervals are called confidence intervals. These measures satisfy properties of good estimator that are namely unbiasedness, consistency and efficiency. They can be used for fitting probability distributions to the data. The parameters of these distributions are also expressed in terms of mean and variance.