March 29, 2018
Single-number statistical measures used to describe random variables are called point estimates. This discussion is limited to random variables which are stationary in time; that is, the point estimates are stable when averaging over a long enough time.
Mean Value. The mean (or “arithmetic average”) value of a set of numbers, xn, n = 1, …, N, is given by
where the over-bar is the notation for the mean value used here.
For many vibration signals, such as the one shown in Fig. 1, the mean value is near zero. This is because the vibration occurs equally in positive and negative directions about a fixed position. Note that the electronics of a vibration transducer usually filter out the “DC” component of a vibration, which is the electrical equivalent of the mean value.