A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information: a.? re there any outliers in the sample? Any extreme outliers? b?. ?Construct a boxplot that shows outliers, and comment on any interesting features.
Solution: Step 1: Here a sample of 20 glass bottles of a particular type was selected. And the internal pressure strength of each bottle is noted. They also given the sample informations. Median=202.2 Three smallest observations = 125.8 188.1 193.7 Upper fourth(3rd quartile)= 216.8 Three largest observations = 221.3 230.5 250.2 Lower fourth(1st quartile) = 196.0 We have to construct a boxplot and want to find is there is any outliers in the Given data. Step 2 : The first and third quartile and the median are part of five number summary of any set of data quantitative data. Here the inner quartile range will be(IQR)=Upper fourth-Lower fourth = 216.8- 196.0 = 20.8 We can obtain the inner and outer fences by Inner fences= 1st quartile- 1.5*(IQR) , 3rd quartile + 1.5*(IQR) = ( 196.0- 1.5*20.8 , 216.0+ 1.5*(20.8) = 164.6, 248 Outer fences = 1st quartile-3(IQR) , 3rd quartile + 3(IQR) = ( 196.0- 3*20.8 , 216.0+ 3*(20.8) = 133.6 , 279.2 In the listed observation based on this IQR,median, 1st quartile,3rd quartile and inner and outer fences , we can tell that the value 125.8 is an extreme low outlier and 250.2 is a mild high outlier.