Arithmetic Average

The risk of an item is reflected in its variability from its average level. For comparison, a stock analyst may want to determine the level of return and the variability in returns for a number of assets to see whether investors in the higher risk assets earned a higher return over time. A financial analyst may want to examine historical differences between risk and profit on different types of new product introductions or projects undertaken in different countries. If historical, or ex-post, data are known, an analyst can easily compute historical average return and risk measures. If Xt represents a data item for period t, the arithmetic average X, over n periods is given by: X ¼ P n t¼1 Xt n : In summary, the sum of the values observed divided by the total number of observation—sometimes referred to as the mean.