  Measurement devices always add noise to the signal of interest and it is
necessary to evaluate the variance of the results. This article focuses on
stationary random processes whose Power Spectrum Density is a power law of
frequency. For flicker noise, behaving as $1/f$ and which is present in many
different phenomena, the usual way to compute the variance leads to infinite
values. This article proposes an alternative definition of the variance which
takes into account the fact that measurement devises need to be calibrated.
This new variance, which depends on the calibration duration, the measurement
duration and the duration between the calibration and the measurement, allows
avoiding infinite values when computing the variance of a measurement.
