The five-number summary below shows the grade distribution of two STAT 200 quizz
ID: 3130847 • 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. Inter quartile range is given by Q3 - Q1
For Quiz 1 , it is 55
For Quiz 2 it is 55
Thus, same fo both (iii)
b.as per definition, Quartile 3 is defined as the value, below which 3/4th of the data is present.
Thus, 1/4th of the data is greater than Quartile 3
1/4th of the data is 500/4 = 150
Thus number of students greater than 85 in case 1 are 150
where as number of students greater than 90 in cae 2 are 150
Thus, clearly,quiz 2 has the greater percentage of students with grades 90 and over (ii)
c. Similarly, Quiz 1 has half of students less than 55
and Quiz 2 has half of students less than 50
Thus there are more number of students, less than 50 in Quiz2 than in Quiz 1
(ii)
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