# Descriptive Statistics

Two students, colleagues at Southeastern University, have obtained the following GPA's for their first 11 courses:

Student/Course # 1 2 3 4 5 6 7 8 9 10 11

Ann 3.5 3.5 4.0 3.5 2.5 3.5 3.0 4.0 3.5 4.0 3.5

Bill 3.0 1.5 4.0 4.0 4.0 3.0 4.0 3.5 1.5 3.5 3.5

1 Determine the 5 number summary for the two distributions

2 Using the 5 number summary determined above, draw, on the same graph, the boxplot representations for the two distributions.

3 You are to choose the proper numerical summary description for each of the two distributions above. What do you choose, and why?

? The 5 number summary, or

? The mean and the standard deviation.

4. For Ann's courses GPA distribution, determine the standard deviation, s.

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5. A medical researcher is testing the effectiveness of a new drug for treating Parkinson's disease. Ten subjects with the disease are given the new drug and 10 are given a placebo. Improvement in symptomology is measured. What would be the roles of descriptive and inferential statistics in the analysis of these data?

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6. What are the advantages and disadvantages of graphical as opposed to numerical approaches to descriptive statistics

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#### Solution Preview

Two students, colleagues at Southeastern University, have obtained the following GPA's for their first 11 courses:

Student/Course # 1 2 3 4 5 6 7 8 9 10 11

Ann 3.5 3.5 4.0 3.5 2.5 3.5 3.0 4.0 3.5 4.0 3.5

Bill 3.0 1.5 4.0 4.0 4.0 3.0 4.0 3.5 1.5 3.5 3.5

1 Determine the 5 number summary for the two distributions.

The five number summary is the following list of numbers:

minimum

1st quartile (number Â¼ of the way down the list if you sort it from smallest to largest)

median (number Â½ way down the list)

3rd quartile (number Â¾ of the way down the list)

maximum

The 5-number summary is below. I have colored the min, median, and max in red. The 1st and 3rd quartiles are the averages of the numbers in italics:

Ann Bill 5-number ...