The fivenumber summary below shows the grade distribution of

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

For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case.

1) Which quiz has less interquartile range in grade distribution?
2) Which quiz has the greater percentage of students with grades 90 and over?
3) Which quiz has a greater percentage of students with grades less than 60?

Solution

1) IQR is Q3-Q1 so 1 is 55 and 2 is 45 so A
2) since the Q3 means the median of the higher 50% of the numbers that means with 1 that at least 25% are 95 or higher (allows for more scores 80-95) and 2 that 25% are 80 or higher so 1 should have a higher percent so A
3) same as 2 but look at the median and since 2 only goes to 50 it should have more scores between 50-60 in between median and Q3 or between the higher 50-75% of scores so B