For any real set of data the variance is bound to be a finite number, but for some theoretical distributions, notably power-law distributions, if you mathematically calculate variance it is infinite. This does impact practical statistics. Normally if you take larger and larger samples the measured variances will nearly always shift closer and closer to some finite value. However, if the underlying distribution is not finite, for example the number of contacts in a social network, then the measured variances of larger and larger samples will tend to become larger and larger.

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