5. The five-number summary below shows the grade distribution of two STAT 200 qu
ID: 3066034 • Letter: 5
Question
5. 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 based on 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 85 and over? (c) Which quiz has a greater percentage of students with grades less than 60?
Minimum Q1 Median Q3 Maximum Quiz 1 15 35 55 85 100 Quiz 2 20 35 50 90 100Explanation / Answer
Initially:
According to box plot:
Min- Q1: 25%
Q1-Q2 : 25%
Q2- Q3 : 25%
Q3 - Max : 25%
IQR= Q3-Q1 : 50%
a) IQR = Q3-Q1
Quiz 1: IQR= Q3-Q1= 85- 35 =50
Quiz 2: IQR= Q3-Q1= 90- 35 = 55
Answer: Quiz 1 has less IQR range
b) Greater percentage over 85 or over?
Quiz 1: > 85 : Q3- Max: 25%
Quiz 2: > 85: Q3-Max + 1*[(90-50)/5]= 25% + 8% =33%
Answer: Quiz 2
c) Quiz has a greater percentage of students with grades less then 60?
Quiz 1: <60: Min to Median+ 1* [(85-55)/5] = 50%+ 6%= 56%
Quiz 2: < 60: Min to median + 2* [(90-50)/5] = 50%+ 16% = 66%
Answer: Quiz 2
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