Question

Two groups of students were asked how many hours they spent reading each day. The table below shows the numbers for each group:

Group A 1 2 1 1 3 3 2 2 3
 Group B 3 2 3 2 2 2 1 1 2
 
Based on the table, which of the following is true?
 
The interquartile range for Group A students is 0.5 less than the interquartile range for Group B students.
 
The interquartile range for Group A students is equal to the interquartile range for Group B students.
 
The interquartile range for Group A employees is 0.5 more than to the interquartile range for Group B students.
 
The interquartile range for Group A employees is 1 more than the interquartile range for Group B students.

Answer 1

Data represented as number of hours spent in studying by Group A Students:

1,2,1,1,3,3,2,2,3

Arranging it in ascending order: 1,1,1 ,2, 2, 2, 3, 3, 3,

As number of terms is odd, The median will be middle value of observation.Which is 2.

The Data arranged in ascending order are , (1,1,1,2),2(2,3,3,3).

Median of (1,1,1,2) =
`Q_(1)`=1

Median of (2,3,3,3)=
`Q_(3)`=3

`D_(1)`=Interquartile Range =
`Q_(3)-Q_(1)`=3-1=2

For Data Set 2,

The Data for group B students are: 3 2 3 2 2 2 1 1 2

Arranging in ascending order: 1,1,2,2,2,2,2,3,3

total number of observation = 9

Median = 2

Arranging the data as : (1,1,2,2) 2,(2,2,3,3)

Median of (1,1,2,2)= Number of observation is 4 which is even , so Median=
`Q_(1)` =
`(1+2)/(2)=(3)/(2)`

Median of (2,2,3,3)=
`Q_(3)`=
`(3+2)/(2)=(5)/(2)`

S=Interquartile Range =
`Q_(3)-Q_(1)`=
`(5)/(2)-(3)/(2)=1`

`D_(1)= S + 1`

Interquartile range for Group A Students =Interquartile range for Group B students + 1

Option (D) The interquartile range for Group A employees is 1 more than the interquartile range for Group B students is true.