The five number summary shows grade distribution of two STAT 200 quizzes for a s

Question

The five number summary shows grade distribution of two STAT 200 quizzes for a samp;e of 500 students quiz 1 minimum of 15 Q1 of 30 median of 55 Q3 of 85 maximum 100 and Quiz 2 with minimum of 20 Q1 of 35 median of 50 Q3 of 90 and maximum of 100. for each question give your answer as one of the following i) quiz 1 ii)quiz 2 iii Both quizzes have same value requested iv)it is impossible to tell using only the given information then explain a) which quiz has less interquartile range in grade dustribution b) which quiz has greater percentage of students with grades 90 or overe c) which quiz has a greater percentage of students with grades less than 50

Explanation / Answer

1) IQR is Q3-Q1 so quiz 1 is 55 and quiz 2 is 55 so Both are having equal IQR

2) since the Q3 means the median of the higher 50% of the numbers that means with 1 that at least 25% are 85 or higher and 2 that 25% are 90 or higher so quiz 2 should have a higher percent.

3) same as 2 but look at the median and since 1 only goes to 50 it should have more scores between 30-35 in between median and Q3 or between the higher 50-75% of scores so Quiz I

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