Respuesta :
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) = [tex]Q_{1}[/tex]=1
Median of (2,3,3,3)=[tex]Q_{3}[/tex]=3
[tex]D_{1}[/tex]=Interquartile Range =[tex]Q_{3}-Q_{1}[/tex]=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=[tex]Q_{1}[/tex] = [tex]\frac{1+2}{2}=\frac{3}{2}[/tex]
Median of (2,2,3,3)=[tex]Q_{3}[/tex]= [tex]\frac{3+2}{2}=\frac{5}{2}[/tex]
S=Interquartile Range = [tex]Q_{3}-Q_{1}[/tex]=[tex]\frac{5}{2}-\frac{3}{2}=1[/tex]
[tex]D_{1}= S + 1[/tex]
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.
