# Mean Square

March 29, 2018

Back to: Random Testing

The mean-square value of a set of numbers, *x _{n}*,

*n*= 1, …,

*N*, is given by the following equation:

(1)

The mean-square value measures the average strength, or power, of a signal. Figure 3.2 plots the square of the vibration signal in Figure 3.1 and shows the mean-square value.

For random signals with a mean value of zero, the mean-square value is the quantity that can be added when summing two signals. This can be seen by considering the sum of two random variables, *A* and* B*. The square of (*A*+*B*) is given by (*A*+*B*)^{2} = *A*^{2} + 2 *A*·*B* + *B*^{2}. If *A* and *B* are independent random variables with zero mean value, the mean value of *A*·*B* is zero. Then the mean square value of the sum is equal to the sum of the mean square values (with zero mean).