Sample Mean and Sample Covariance

Sample Mean And Sample Covariance

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 variables – that 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).