The five-number summary below shows the grade distribution of two STAT 200 quizz
ID: 3131068 • Letter: T
Question
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: (i) Quiz 1; (ii) Quiz 2; (iii) Both quizzes have the same value requested; (iv) It is impossible to tell using only the given information. Then explain your answer in each case.
(a) Which quiz has less interquartile range in grade distribution?
(b) Which quiz has the greater percentage of students with grades 90 and over?
minimum
Q1
median
Q3
maximum
Quiz 1
15
30
55
85
100
Qui 2
20
35
50
90
100
minimum
Q1
median
Q3
maximum
Quiz 1
15
30
55
85
100
Qui 2
20
35
50
90
100
Explanation / Answer
a. Interquartile range for :
Quiz 1 = Q3 -Q1 = 85 - 30 = 55
Quiz 2 = Q3 - Q1 = 90 - 35 = 55
b. For Quiz 1, 25% students have marks greater than 85 (Q3), so less than 25% students have marks greater than 90.
For Quiz 2, 25% students have marks greater than 90 (Q3)
So, Quiz 2 has the greater percentage of students with grades 90 and over.
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