Question

Calculate Q. D. for the following data:

X	24	25	26	27	28	29	30
F	6	5	3	2	4	7	3

Answer 1

X	F	c.f. (less than type)
24	6	6
25	5	11 ← Q1
26	3	14
27	2	16
28	4	20
29	7	27 ← Q3
30	3	30
Total	30

Here, N = 30

Q₁ = value of `(("N" + 1)/4)^"th"` observation

= value of `((30 + 1)/4)^"th"` observation

= value of (7.75)^th observation

Cumulative frequency which is just greater than (or equal to) 7.75 is 11.
∴ Q₁ = 25

Q₃ = value of `[3(("n" + 1)/4)]^"th"` observation

= value of `[3((30 + 1)/4)]^"th"` observation

= value of (3 × 7.75)^th observation
= value of (23.25)^th observation

Cumulative frequency which is just greater than (or equal to) 23.25 is 27.
∴ Q₃ = 29

∴ Q.D. = `("Q"_3 - "Q"_1)/(2)`

=  `(29 - 25)/(2)`

= `(4)/(2)`
∴ Q.D. = 2