The
sample mean or
empirical mean and the
sample covariance are
statistics computed from a collection of data on one or more
random variables. The sample mean is a
vector each of whose elements is the sample mean of one of the random variablesthat is, each of whose elements is the
arithmetic average of the observed values of one of the variables. The sample covariance matrix is a square
matrix whose
i, j element is the sample covariance (an estimate of the population covariance) between the sets of observed values of two of the variables and whose
i, i element is the sample variance of the observed values of one of the variables. If only one variable has had values observed, then the sample mean is a single number (the arithmetic average of the observed values of that variable) and the sample covariance matrix is also simply a single value (the sample variance of the observed values of that variable).