The five-number summary below shows the grade distribution of two STAT 200 quizz

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 you answer in each case
Minimum Q1 Median Q3 Maximum
Quiz 1 15 35 55 85 100
Quiz 2 20 35 50 90 100

Which quiz has less interquartile range in grade distribution?

Which quiz has the greater percentage of students with grades 85 and over?

Which quiz has a greater percentage of students with grades less than 60?

Explanation / Answer

Which quiz has less interquartile range in grade distribution?

For quiz 1,

IQR = Q3 - Q1 = 85-35 = 50

For quiz 2,

IQR = Q3 - Q1 = 90-35 = 55

HENCE, QUIZ 2 HAS A HIGHER INTERQUARTILE RANGE. [ANSWER]

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Which quiz has the greater percentage of students with grades 85 and over?

For quiz 1, Q3 = 85. Hence, exactly 25% of data is 85 and over.

For quiz 2, Q3 = 90. Hence, more than 25% of data is 85 and over.

Hence, QUIZ 2 has the greater percentage of students with grades 85 and over. [ANSWER]

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Which quiz has a greater percentage of students with grades less than 60?

None of the markers is equal to 60. Hence, it is impossible to tell. [ANSWER]

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