Question

Consider the following observations on shear strength (MPa) of a joint bonded in a particular manner 21.0 40.4 16.4 72.26.6 110.0 30.0 4.4 33.166.7 81.5 (a) What are the values of the fourths? (Enter your answers to two decimal places.) lower fourth 25.50 upper fourth 69.45 MPa MPa What is the value of f? 43.95 MPa (b) Construct a boxplot based on the five-number summary. 40 60 80 40 60 80 100 O 20 20

please just complete answer (d)

Answer 1

The data in increasing order is given by

4.4 16.4 21.0 30.0 33.1 36.6 40.4 66.7   72.2 81.5 110.0

So the largest observation (that is 110) can be decreased to the value of 9th observation in increasing order (that is 72.2), because in that case the value of upper fourth remains the same. We can see that 8th and 9th observations are being used to calculate the upper fourth. So, the largest observation can decrease until the 8th and 9th observations remain the same.

And hence the value of $f_s$ (that is Inter Quartile Range) remains the same.

So largest value can be decreased by :

110.0 - 72.2 = 27.8 (answer)