Question

Calculate the quartile deviation and its coefficient from the following data:

Age in Years:	20	30	40	50	60	70	80
No. of Members:	13	61	47	15	10	18	36

Answer 1

Age in Years (X)	No. of Members (f)	Cumulative Frequency (cf)
20	13	13
30	61	74
40	47	121
50	15	136
60	10	146
70	18	164
80	36	200
	N = ∑f = 200

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

= Size of `((200 + 1)/4)^"th"` value

= Size of `(201/4)^"th"` value

= Size of 50.25^th value

Q₁ = 30

Q₃ = Size of `((3("N" + 1))/4)^"th"` value

= Size of `((3 xx 202)/4)^"th"` value

= Size of `(606/4)^"th"` value

= Size of 151.5^th value

Q₃ = 70

QD = `1/2 ("Q"_3 - "Q"_1)`

= `1/2 (70 - 30)`

= `1/2 xx 40`

QD = 20

Coefficient of QD = `("Q"_3 - "Q"_1)/("Q"_3 + "Q"_1)`

= `(70 - 30)/(70 + 30)`

= `40/100`

= 0.4