Question

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

Answer 1

Solution:

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=$Q_{1}$ =  $\frac{1+2}{2}=\frac{3}{2}$

Median of (2,2,3,3)=$Q_{3}$= $\frac{3+2}{2}=\frac{5}{2}$

S=Interquartile Range = $Q_{3}-Q_{1}$=$\frac{5}{2}-\frac{3}{2}=1$

$D_{1}= S + 1$

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.

Answer 2

D) The interquartile range for group a employees is 1 more than than the t interquartile range of Group B students.