Question

The table below has a total of 56 values.  Find the 4^th decile for the following Grouped Frequency Data Table (GFDT).

Lower Class Limit	Upper Class Limit	Frequency
70	74	5
75	79	7
80	84	6
85	89	3
90	94	6
95	99	10
100	104	4
105	109	9
110	114	6

The 4^th decile =

Answer 1

Solution:

Class	Frequency f	cf
70 - 74	5	5
75 - 79	7	12
80 - 84	6	18
85 - 89	3	21
90 - 94	6	27
95 - 99	10	37
100 - 104	4	41
105 - 109	9	50
110 - 114	6	56
	n = 56

Here, n=56


D₄ class :

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

=((4⋅56) /10)^th value of the observation in cf column

=(22.4)^th value of the observation in cf column

and it lies in the class 90-94.

∴D₄ class : 90-94

The lower boundary point of 90-94 is 89.5.

∴L=89.5

D₄=L+((4*n) /10-cf )f⋅c

=89.5+(22.4-21)/6 ⋅5

=89.5+(1.4/6)⋅5

=89.5+1.1667

=90.6667

D₄= 90.67