Question

11. The following data are the hemoglobin measurements (in g/dL) for 20 randomly selected cats. Find the five-number summary, construct a boxplot for the data and 20th and 70th percentiles. Are there any outliers? 5.7 7.7 7.8 8.7 8.9 9.4 9.5 9.6 9.6 9.9 10.0 10.3 10.6 10.7 11.0 11.2 11.7 12.9 13.0 13.4

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Answer #1

from above minimum =5.7

first quartile =(n+1)*p th value=21*0.25 th value =5.25 th value =(8.9+0.25*(9.4-8.9)=9.025

median ==21*0.5 th value =10.5 th value =(9.9+10)/2=9.95

quartile 3==21*0.75 th value =16.75 th value =11.2+0.75*(11.7-11.2)=11.575

maximum =13.4

hence 5 number summary is : 5.7 ; 9.025 ; 9.95 ; 11.575 ; 13.4

from above lower fence =Q1-1.5*(Q3-Q1)=9.025-1.5*(11.575-9.025)=5.2

also upper fence=Q3-1.5*(Q3-Q1)=11.575+1.5*(11.575-9.025)=15.4

as 5.7 is outside the fence limits ; it is an outlier

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