Blindly making measurements and taking averages or computing variances is NOT a sensible thing to do! It particularly meaningful for the Gaussian distribution,

Blindly making measurements and taking averages or computing variances is NOT a sensible thing to do! It particularly meaningful for the Gaussian distribution, but there is no reason for sociological data to have such behavior! The essence of the technical argument is that sample moments (such as the variance or even the mean, for the most extreme cases) are not meaningful quantities for the more heavy-tailed power laws. Therefore, the empirically measured "sample mean" then does not correspond to any meaningful characteristic of the actual distribution.