# Skewness

March 29, 2018

Back to: Random Testing

**Skewness.** The skewness of a set of numbers, *x _{n}*,

*n*= 1, …,

*N*, is given by

The skewness is a measure of the asymmetrical spread of a signal about its mean value. It is the ratio of the average cubed deviation from the mean divided by the cube of the standard deviation. Therefore, it is dimensionless. For a random variable with a *Normal distribution* the skewness is zero (see the lesson on Normal (Gaussian) Distribution).

Fig. 3 shows the turbulent pressure measured on the outside of the skin of an aircraft in flight. The pressure fluctuates more negatively than positively from the mean value giving the skewness a value of γ = -0.32 (with a mean value of -0.03 kPa and a standard deviation of 1.08 kPa). Note that the true mean value of the pressure (the atmospheric pressure, *p _{atm}*) has been taken out of the signal electronically, so the measured signal is actually (

*p*

_{ – }

*p*) and has a mean value near zero.

_{atm}