Question

The following table shows the number of hours some teachers in two schools expect students to spend on homework each week.

School A

9

14

15

17

17

7

15

6

6

School B

12

8

13

11

19

15

16

5

8

Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (5 points)
Part B: Are there any outliers present for either data set? Justify your answer mathematically. (5 points) (10 points)

Answer 1

Part A: School A Interquartile range = 9.5. School B Interquartile range = 7.5

Part B: There are no outliers present for either data set.

Explanation:

For Part A, school A interquantile range is 9.5. Five number summary of school A is minimum = 6, quarantine q1= 6.5, median = 14, quarantine q3 = 16, and maximum = 17. Calculate Q3-Q1 = 16 - 6.5 which gives you 9.5

For School B, the interquartile range is 7.5. Five number of summary of school B is minimum = 5, quarantine q1 = 8, median = 12, quarantine q3= 15.5, maximum = 19. IQR Range = Q3-Q1 = 15.5 - 8. Which gives you 7.5

For Part B: All the outcomes of school A in between the values of -7.75 and 30.25. So this means there is no outliers in school A. For school B, all the outcomes of school B in between the values of -3.25 and 26.75. So there are no outlines in school B.