An engineer is studying bearing failures for two different materials in aircraft gas turbine engines. The following data are failure times (in millions of cycles) for samples of the two material types.

(a) Determine the sample mean failure time for each material.
(b) By hand, compute the median failure time for each material.
(c) Determine the sample standard deviation of the failure times for each material. Which material has its failure times more dispersed?
(d) By hand, compute the five-number summary for each material.
(e) On the same graph, draw boxplots for the two materials. Annotate the graph with some general remarks comparing the failure times.
(f) Describe the shape of the distribution of each material using the boxplot and quartiles.

Material A 3.17 4.31 4.52 4.66 5.69 Material B 5.88 5.78 6.916.71 8.01 6.84 8.97 7.23 11.92 8.20 9.65 13.44 14.71 16.39 24.37