Question

Lower Class Limit	Upper Class Limit	Frequency
60	64	3
65	69	7
70	74	3
75	79	7
80	84	7
85	89	11
90	94	10
95	99	9
100	104	12

(a) What is the 11^th percentile for the following Grouped Frequency Data Table?

(b) What is the 4^th decile for the following Grouped Frequency Data Table?

Answer 1

Solution:

Class	Frequency f	cf
60 - 64	3	3
65 - 69	7	10
70 - 74	3	13
75 - 79	7	20
80 - 84	7	27
85 - 89	11	38
90 - 94	10	48
95 - 99	9	57
100 - 104	12	69
	n = 69

a ) P₁₁ class :

Class with (11 *n ) /100)^th value of the observation in cf column

=(11⋅69 /100)^th value of the observation in cf column

=(7.59)^th value of the observation in cf column

and it lies in the class 65-69.

∴P₁₁ class : 65-69

The lower boundary point of 65-69 is 64.5.

∴L=64.5

P₁₁= L+( (11 *n ) /100-cf) / f ) *c

=64.5+( (7.59-3 ) /7)⋅5

=64.5+(4.59 /7)⋅5

=64.5+3.2786

=67.7786

P₁₁= 67.78

b ) D₄ class :

Class with ((4*n) /10)^th value of the observation in cf column

=((4⋅69)10)^th value of the observation in cf column

=(27.6)^th value of the observation in cf column

and it lies in the class 85-89.

∴D₄ class : 85-89

The lower boundary point of 85-89 is 84.5.

∴L=84.5

D₄=L+((4 *n) /10 -cf / f ) ⋅c

=84.5+((27.6)-27/11)⋅5

=84.5+(0.6/11)⋅5

=84.5+0.2727

=84.7727

D₄= 84.77