Mean Value

March 29, 2018

Single-number statistical measures that 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*}

Equation 1

For many vibration signals, such as the one 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.

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).

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.