The five-number summary below shows the grade distribution of two STAT 200 quizz
ID: 3131170 • Letter: T
Question
The five-number summary below shows the grade distribution of two STAT 200 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: (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?
(c) Which quiz has a greater percentage of students with grades less than 50?
Minimum
Q1
Median
Q3
Maximum
Quiz 1
15
30
55
85
100
Quiz 2
20
35
50
90
100
Explanation / Answer
(a) Which quiz has less interquartile range in grade distribution?
Quiz 1 = Q3 - Q 1 = 85 - 30 = 55
Quiz 2 = Q3 - Q1 = 90 - 35 = 55
Both QUIz has similar inter quartile range
(b) Which quiz has the greater percentage of students with grades 90 and over?
It is Quiz 2, as the reason Q3 = 90, i.e 75% of scores are below 90. we have
25% scored scores are above to 90
(c) Which quiz has a greater percentage of students with grades less than 50?
It is impossible to tell using only the given information, because Median of Quiz 1
is 55 and we cleary knows that 50% of data is less than 55 and it may possible that
most of the scores in between 50 < X < 55.
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