Use the following set of data-management final examination scores to answer the following questions:

75, 98, 56, 54, 63, 55, 67, 61, 96, 45, 62, 68, 48, 52, 60, 59, 92, 68, 72, 71

a) Determine the quartiles [Q1 and Q3] , the inter-quartile range, and the semi-inter-quartile range for the above data. Show your calculations.

b)Create a box-and-whisker plot for this distribution. Make sure you show all necessary calculations. Use a ruler and include appropriate labels and a scale.

c)if the math department wants to give an award to the students in the 90th percentile and above, what score should the math department use as a cut-off?