Mean Value

March 29, 2018

Single-number statistical measures used to describe random variables are called point estimates. This discussion is limited to random variables that are stationary in time; that is, the point estimates are stable when averaging over a long enough time.

Mean Value Equation

The mean value of a set of numbers, xnn = 1, …, N,  is given by the following equation:

(1)   \begin{equation*} \bar{x}=\frac{1}{N}\sum_{n=1}^{N}x_{n} \end{equation*}

For many vibration signals, such as the one shown in Figure 3.1, 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.

Random vibration signal (acceleration of car floor at 120 km/h)

Figure 3.1. Random vibration signal (acceleration of car floor at 120 km/h).