The five-number summary below shows the grade distribution of two ST AT 200 quiz

Question

The five-number summary below shows the grade distribution of two ST AT 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. Which quiz has less interquartile range in grade distribution? Which quiz has the greater percentage of students with grades 90 and over? Which quiz has a greater percentage of students with grades less than 50?

Explanation / Answer

(a) (iii) Both quizzes have the same value as requested

interquartile range of Quiz 1 = Q3-Q1 = 85-30 =55

interquartile range of Quiz 2 = Q3-Q1 = 90-35 =55

(b) (iv) It is impossible to tell using only the given information

Eventhough considering Q3 we cannot get since the Q3 means the median of the higher 50% of the numbers that means above Q3 corresponds to top 25% this gives us information regarding above grades 75 or more but not 90 or more.

(c) (i) Quiz 11

For Quiz 1 below Median = 55

For Quiz 1 below Median = 50

As 55> 50

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