Reference no: EM132853115
We consider the following final grade data for 90 STAT 221 students:
99, 96, 95, 94, 94, 93, 93, 92, 92, 92, 88, 87, 87, 86, 86, 86, 86, 85, 85, 85, 82, 81, 81, 80, 80, 79, 79, 79, 78, 78, 73, 73, 72, 71, 71, 70, 70, 70, 69, 69, 61, 60, 59, 57, 54, 54, 53, 48, 47, 42, 91, 91, 91, 90, 85, 85, 84, 84, 77, 77, 77, 76, 68, 68, 68, 67, 90, 90, 89, 89, 88, 88, 84, 83, 83, 82, 82, 82, 76, 75, 75, 75, 74, 74, 66, 66, 65, 64, 64, 63
(a) Calculate the sample mean x and sample standard deviation s for the given sample data. Show all your work for full credit.
(b) Provide the five-number summary as well as the IQR for this data. All calculations should be performed by hand. Show all your work for full credit.
(c) Use R to construct a relative frequency histogram and comment on the skewness of the given sample data. Include your R-code and the corresponding output as a part of your answer.
(d) Use R to construct a qqplot for the sample data. Include your R-code and the corresponding output as a part of your answer.
(e) Using both the numerical and graphical summaries for these data, assess whether it is reasonable to assume a Gaussian model for these data. You must support your conclusion with reasons written in complete sentences and not in point form.