Chapter 6

Data sets

Covariance is a measure of linear association and the correlation coefficient is its non-dimensional form. We explain sample covariance and population covariance in the context of bivariate probability distributions. We derive formulae for the mean and variance of a linear combination of random variables in terms of their means, variances and pair-wise covariances. A special case of this result is that the mean of a simple random sample of size n from a population with mean μ and variance σ² has a mean of μ and a variance σ²/n. We state the Central Limit Theorem and discuss the consequence that the sample mean has an approximate normal distribution.