Need Help?

Subscribe to Probability

  • Notes
  • Comments & Questions

Preventing fatigue crack propagation in aircraft struc-
tures is an important element of aircraft safety. An engineering
study to investigate fatigue crack in $$n=9$$ cyclically loaded
wing boxes reported the following crack lengths (in $$\mathrm{mm}$$ )
$$2.13,2.96,3.02,1.82,1.15,1.37,2.04,2.47,2.60 .$$

(a) Calculate the sample mean.
(b) Calculate the sample variance and sample standard


crack lengths:


(a) Calculate sample mean.

$$\overline{x}=\frac{\sum_{i=1}^{n} x_{i}}{n}=\frac{19.56}{9}=2.173 \mathrm{mm}$$

(b) sample variance

$$S^{2}=\frac {\sum_{i=1}^{n} {x_{i}^{2}-\frac {\left(\sum x_{i}\right)^{2}}{n}}}{n-1}$$

$$\sum x_{i}=19.56 \mathrm {m m}$$

$$\sum x_{i}^{2}=45.953 \mathrm{mm}^{2}$$


$$=\frac{3.443}{8}=0.4303 \mathrm{mm}^{2}$$

$$S=\sqrt{s^{2}}=0.6560 \mathrm{mm}$$

No comments yet

Join the conversation

Join Notatee Today!