Making Investment Decisions Under Uncertain Conditions 278 Therefore, Excel provides two functions that return a standard deviation. If you're working with a sample, you should use the STDEV function. If you're working with a population, use the STDEVP function instead, =STDEVP(A1:A20) where the P at the end of the function name is a mnemonic for "Population." Applied to a sample, the proper formula is Notice that the denominator of the ratio is now (n­1): the number of observations minus 1. STDEV uses (n­1) in the denominator, whereas STDEVP uses n in the denominator. CAUTION Be cautious when you use STDEV or STDEVP on data whose magnitude is either very large (on the order of, say, 10^5 or greater) or very small (say, 10^-5 or smaller). With such data, rounding errors can occur in any PC application, not just Excel, because of the cumulative effect of squaring the differences between the observations and their mean. If you work with data such as this, you might consider re-scaling the numbers before applying STDEV or STDEVP, and interpreting their results in terms of the re-scaling. Finding the standard deviation of a set of numbers enables you to make precise statements about their variability. This knowledge by itself can be useful. Suppose your company manufactures equipment that must fall within certain physical limits, such as diameters. In that case, you need to know whether the variability of your product line's diameters is comfortably inside those limits or is