The following applies to these procedures in Base SAS^®: MEANS, UNIVARIATE, SUMMARY, TABULATE, REPORT, STANDARD, and CORR.

When you use the WEIGHT statement, the ith observation is assumed to have variance σ²/w_i, where w_i is the weight of the ith observation. When the VARDEF=DF (the default) option is specified, the variance is an estimate of σ². This yields an estimate of the variance of an observation with unit weight (that is, w_i =1). To get an estimate of each observation's variance, divide the VARDEF=DF variance estimate by the observation's weight, w_i.

When you use the WEIGHT statement and the VARDEF=WGT option, the computed variance is asymptotically (for large n) an estimate of σ²/avg(w), where avg(w) is the average weight. This yields an asymptotic estimate of the variance of an observation with average weight. This might be of interest as an estimate of the variance of a "typical" observation.