Abstract
Inequalities involving some sample means and order statistics are established. An upper bound of the absolute difference between the sample mean and median is also derived. Interesting inequalities among the sample mean and the median are obtained for cases when all the observations have the same sign. Some other algebraic inequalities are derived by taking expected values of the sample results and then applying them to some continuous distributions. It is also proved that the mean of a non-negative continuous random variable is at least as large as p times 100(1 − p)th percentile.