Question

The following table shows the number of hours some students in two universities spend reading each week:

School A : 7 2 3 10 17 14 10 22 2
School B : 9 10 16 18 20 15 17 18 14


Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)

Part B: Are the box plots symmetric? Justify your answer. (4 points)

Answer 1

Part 1:

Interquartile range: (A = 13, B = 6)

Five-number summary:

A = (2,12,10,18,22) B = (13,9,16,20,6)

Part 2:

The box plots are not symmetric.

Answer 2

Part A- Interquartile range of school A = 13 and school B= 6

Part B- They are not symmetric.

Explanation:

Given : Data that shows the number of hours some students in two universities spend reading each week:

School A : 7 2 3 10 17 14 10 22 2

School B : 9 10 16 18 20 15 17 18 14

To find :

Part A: Create a five-number summary and calculate the inter quartile range for the two sets of data.

Part B: Are the box plots symmetric?

Solution : First arrange the data set in ascending order:

School A: 2, 2, 3, 7, 10, 10, 14, 17, 22

School B: 9, 10, 14, 15, 16, 17, 18, 18, 20

1) Part A - To create five- number summary:

→For School A-

The median is 10.

Therefore, the lower half of the data is: {2,2,3,7}.

The first quartile,
`Q_1`, is the median of {2,2,3,7}.

Since there is an even number of values, we need the mean of the middle two values to find the first quartile:

`Q_1= (2+3)/(2)=(5)/(2)=2.5`

Similarly, the upper half of the data is: {10,14,17,22}, so

`Q_3= (14+17)/(2)=(31)/(2)=15.5`

→Similarly for School B

The median is 16.

Therefore, the lower half of the data is: {9,10,14,15}.

The first quartile,
`Q_1`, is the median of {9,10,14,15}.

Since there is an even number of values, we need the mean of the middle two values to find the first quartile:

`Q_1= (10+14)/(2)=(24)/(2)=12`

Similarly, the upper half of the data is: {17,18,18,20}, so

`Q_3= (18+18)/(2)=(36)/(2)=18`

Inter quartile range is
`IQR=Q_3-Q_1`

School A School B

minimum 2 9

`Q_1` 2.5 12

median 10 16

`Q_3` 15.5 18

maximum 22 20

IQR 13 6

2) Part B- The box plot are not symmetric. The distance of the median from each
`Q_1` and
`Q_3`should be equal for the box plot to be symmetric.