Preventing fatigue crack propagation in aircraft structures is an important elem

Question

Preventing fatigue crack propagation in aircraft structures 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 mm): 2.13, 2.96, 3.02, 1.82, 1.15, 137,2.04, 247, 2.60. For this data, do the following: (a) Calculate the sample mean and sample standard deviation by hand. b) Make a stem-and-leaf diagram by hand using all the digits. Use an increment of 1 for the stems. (c) Make a stem-and-leaf diagram with 2-line-per-stem by hand using all the digits (an increment of 0.5 for the stems) (d) Calculate the sample median by hand with the help of your stem-and-leaf diagram in part (b) or (c). e) Repeat parts (a) - (d using R. Please note that the stem plots done by R will not be exactly the same as the ones you made by hand in parts (b) and (c) because R only gives one digit for a leaf. Show R codes and outputs.

Explanation / Answer

a. Sample mean, xbar=summation x/n=(2.13+2.96+...+2.60)/9=19.560/9=2.173; sample standard deviation, s=sqrt[1/n-1 summation (x-xbar)^2]=sqrt[1/9-1 {(2.13-2.173)^2+...+(2.60-2.173)^2}]=0.656

b. The stem and leaf plot is as follows:

1 138

2 01469

3 0

Lgend:1|1 read1.15

c. The stem and leaf plot is as follows:

1 13

1 18

2 014

2 69

3 0

Legend:1|1 reads as 1.15.

d. For odd numbered data, n=9, sample median will be the value corresponding to middle most data, that is 5th value. Locate the 5th value in the stem plot (stem plot for part b is easier to interpret). The median is read as 2.13.

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