Minimum Q1 Median Q3 Maximum Quiz 1 15 45 55 85 100 Quiz 2 2

Minimum

Q1

Median

Q3

Maximum

Quiz 1

15

45

55

85

100

Quiz 2

20

35

50

90

100

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

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)

Which quiz has less interquartile range in grade distribution?

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

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

2. A combination lock uses three distinctive numbers between 0 and 49 inclusive. How many different ways can a sequence of three numbers be selected? (Show work) (5 pts)

Solution

Which quiz has less interquartile range in grade distribution?

For quiz 1: IQR = Q3-Q1 = 85-45 = 40
For quiz 2: IQR = Q3-Q1 = 90-35 = 55

Thus, QUIZ 1 has less IQR.

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

As Q3(quiz 1) < 90, and Q3(quiz 2)= 90, then there should be more students with grades 90 and over for QUIZ 2. [ANSWER, QUIZ 2]

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

As none of the quartiles is exactly 60, then it is OPTION D: IMPOSSIBLE TO TELL USING ONLY THE GIVEN.

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