Question

Calculate the IQR for both groups. What do the IQRs reveal about the degree diversity for males and females?

Answer 1

Solution:-

Male(in ascending order)=

28

56

68

106

267

525

Median=(68+106)/2=87

Lower Quartile(Q₁)= median of the lower half of the data

Here, Lower Half data:-

28

56

68

Lower Quartile(Q₁)=56

Upper Quartile(Q3)=median of the upper half of the data

Here, upper Half data:-

106

267

525

Upper Quartile(Q3)=267

now, IQR(Inter Quartile Range)=Q3-Q₁=267-56

=211 ...ans

Female (in ascending order)=

61

73

84

120

316

654

Lower Quartile(Q₁)= median of the lower half of the data

Here, Lower Half data:-

61

73

84

Lower Quartile(Q₁)=73

Upper Quartile(Q3)=median of the upper half of the data

Here, upper Half data:-

120

316

654

Upper Quartile(Q3)=316

now, IQR(Inter Quartile Range)=Q3-Q₁=316-73

=243 ...ans

IQR, reveals how the middle 50% of data are distributed.