chapter 1

Chapter 1: Overview and Descriptive Statistics75.a. The median is the same (371) in each plot and all three data sets are very symmetric. Inaddition, all three have the same minimum value (350) and same maximum value (392).Moreover, all three data sets have the same lower (364) and upper quartiles (378). So, allthree boxplots will be identical.b. A comparative dotplot is shown below. These graphs show that there are differences inthe variability of the three data sets. They also show differences in the way the values aredistributed in the three data sets.. .: . ::: . :.-----+---------+---------+---------+---------+---------+- Type 1. . . . . .. . . . . . . . .-----+---------+---------+---------+---------+---------+- Type 2.. . . :. . . : .: .-----+---------+---------+---------+---------+---------+- Type 3352.0 360.0 368.0 376.0 384.0 392.0c. The boxplot in (a) is not capable of detecting the differences among the data sets. Theprimary reason is that boxplots give up some detail in describing data because they useonly 5 summary numbers for comparing data sets. Note: The definition of lower andupper quartile used in this text is slightly different than the one used by some otherauthors (and software packages). Technically speaking, the median of the lower half ofthe data is not really the first quartile, although it is generally very close. Instead, themedians of the lower and upper halves of the data are often called the lower and upperhinges. Our boxplots use the lower and upper hinges to define the spread of the middle50% of the data, but other authors sometimes use the actual quartiles for this purpose.The difference is usually very slight, usually unnoticeable, but not always. For examplein the data sets of this exercise, a comparative boxplot based on the actual quartiles (ascomputed by Minitab) is shown below. The graph shows substantially the same type ofinformation as those described in (a) except the graphs based on quartiles are able todetect the slight differences in variation between the three data sets.Type of wire321350360370MPa38039040