Here is a description from Minitab of the strength data given in Exercise 13. a. Comment on any interesting features (the quartiles and fourths are virtually identical here). b. Construct a boxplot of the data based on the quartiles, and comment on what you see. Reference exercise -13 Allowable mechanical properties for structural design of metallic aerospace vehicles requires an approved method for statistically analyzing empirical test data. The article “Establishing Mechanical Property Allowables for Metals” (J. of Testing and Evaluation, 1998: 293–299) used the accompanying data on tensile ultimate strength (ksi) as a basis for addressing the difficulties in developing such a method. a. Construct a stem-and-leaf display of the data by first deleting (truncating) the tenths digit and then repeating each stem value five times (once for leaves 1 and 2, a second time for leaves 3 and 4, etc.). Why is it relatively easy to identify a representative strength value? b. Construct a histogram using equal-width classes with the first class having a lower limit of 122 and an upper limit of 124. Then comment on any interesting features of the histogram.
Answer : Step 1 : Here is a description from Minitab of the strength data given. N Mean Median Tr Std Dev SE Variable Mean Mean 153 135.39 138.25 135.41 4.59 0.4 Strength Variable Minimum Quartile 1 Quartile 2 Maximum 122.2 132.95 135.4 147.7 Strength a). From the known minitab output,the mean median and trimmed mean are nearly identically. This indicates that there is substantial amount of symmetry in the data. The fact that the quartiles are nearly the same distance from the median and that the smallest and largest are roughly equidistant from the centre provides additional support for symmetry. The standard deviation is quite small relative to the mean and median. The range of values is only 25.5, but half of the values are between 132.95 and 138.25.