The fivenumber summary below shows the grade distribution of

The five-number summary below shows the grade distribution of two STAT 200 quizzes for a sample of 500 students.

Quiz 1 -   15 / 45 / 55 / 85 / 100

Quiz 2 - 20 / 35 / 50 / 90 / 100

For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case. (4 pts each)

8. Which quiz has less interquartile range in grade distribution?

9. Which quiz has the greater percentage of students with grades 90 and over?

10. Which quiz has a greater percentage of students with grades less than 60?

Solution

8.

As

IQR = Q3-Q1

Then

Quiz 1: IQR = 85 - 45 = 40
Quiz 2: IQR = 90 - 35 = 55

Thus, QUIZ 1 has less IQR. [ANSWER, QUIZ 1]

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9.

As Q3 of Quiz 1 is less than Q3 of Quiz 2, which is exactly 90, then QUIZ 2 must have the greater percentage of students with grades 90 and over.
[ANSWER, Quiz 2]

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10.

OPTION D: It is impossible to tell using only the given information.

This is so because none of the given data is exactly 60. There is so much we don\'t know in between those numbers given, so we cannot tell.