Skewness

March 29, 2018

The skewness of a set of numbers, xn= 1, …, N, is given in Equation 7:

(1)   \begin{equation*} \gamma=\frac{1}{N\sigma^3}\sum_{n=1}^{N}(x_{n}-\mu)^3 \cong \frac{\frac{1}{N} \sum_{n=1}^{N} (x_{n}-\bar{x})^3}{(\frac{1}{N} \sum_{n=1}^{N} (x_{n}-\bar{x})^2)^{3/2}} \end{equation*}

Equation 7

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 normal distribution, the skewness is zero (visit the lesson on Normal (Gaussian) Distribution.)

Figure 3.3 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, patm) has been taken out of the signal electronically, so the measured signal is actually (p – patm ) and has a mean value near zero.

Turbulent pressure measured on the outside of the skin of an aircraft in flight

Figure 3.3. Turbulent pressure measured on the outside of the skin of an aircraft in flight.