Refer to the following situation for Questions 89and 10 The

Refer to the following situation for Questions 8,9,and 10. 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.

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

9.Which quiz has the greater percentage of students with grades 80 or over?

10. Which quiz has a greater percentage of students with grades less than or equal to 50?

Solution

Q8.
IQR for Quiz 1 = 85-30= 55
IQR for Quiz 2 = 90-35 = 55
Thus Quiz 1 has lower IQR value.

(c) Both quizzes
have the same value requested

Q9.
Q3 for Quiz 1 is 85 thus more than 25% of the values are over 80 for quiz 1 and Q3, for Quiz 2 is 90 so 25% of the values are over 90 for quiz 2.
Hence Quiz 2 has the greater percentage of students with grades 80 and over.

Q10.

Quiz 1 has median 55 and Quiz 2 has median 50 thus assuming the variation is equal Quiz 2 has larger percentage of students with grades less than 50.