**by Jörgen
Dalén**

**Research Report
1999:1**

Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden

**Abstract**

For the lognormal distribution an exact expression for the variance of the geometric mean is derived and it is proved that this variance is always smaller than that of the arithmetic mean. Through Taylor expansions, a rule of thumb is worked out which is approximately valid for distributions of price ralatives and other positive variables with small or moderate coefficients of variation.

**Key words:** Price index,
lognormal distribution, Taylor expansions.

*Last update: 1999-09-16/CE*