The fivenumber summary below shows the grade distribution of

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

Minimum

Q1

Median

Q3

Maximum   

Quiz 1

15

30

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.

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?

Solution

Which quiz has less interquartile range in grade distribution?

BOTH QUIZES HAVE THE SAME VALUE

IRQ = Q3 - Q1

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

It is impossible to tell using only the given information.

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

QUIZ 1 BECAUSE THE MEDIAN IS GREATER THAN QUIZ 2