Preventing fatigue crack propagation in aircraft structures is an important element of aircraft safety. An engineering study to investigate

fatigue crack in n = 9 studies reports the following crack lengths (in mm):

2:42 1:77 3:18 1:19 2:34 5:95 0:63 3:30 3:45.

1. Compute the sample mean, median, range, sample variance, sample stan-dard deviation, Q₁ , Q₃ and IQR.
2. Prepare a box plot. Are there any outliers? Please clearly label your plot.
3. Add each measurement by 2.25 and then divide the result by 1.5, i.e., for 2.42, it now becomes (2:42+2:25)=1:5. Now compute the sample standard deviation for the new data. How is this quantity related to the standard deviation of the original data? Explain why.