Question

For the following frequency distribution find:
(i) Lower quartile
(ii) Upper quartile
(iii) Inter quartile range
(iv) Semi-inter quartile range.

x	1	2	3	4	5	6	7	8
y	3	5	9	15	20	16	10	2

Answer 1

x	f	Cumulative frequency
1	3	3
2	5	8
3	9	17
4	15	32
5	20	52
6	16	68
7	10	78
8	2	80
		n = 80

(i) Lower quartile
(Q₁) = The value of `("n"/4)^"th"` observation
= The value of `(80/4)^"th"` observation
= The value of 20^th observation
Q₁ = 4.
(ii) Upper quartile
(Q₃) = The value of `((3"n")/4)^"th"` observation
= The value of `((3 xx 80)/4)^"th"` observation
= The value of 60^th observation
∴ Q₃ = 6.
(iii) Inter quartile range
= Q₃ - Q₁
= 6 - 4
= 2.
(iv) Semi-quartile range
= `(Q_3 - Q_1)/(2)`
= `(2)/(2)`
= 1.