Question

Calculate Quartile deviation and Coefficient of Quartile deviation of the following data.

Marks:	0	10	20	30	40	50	60	70
No. of students:	150	142	130	120	72	30	12	4

Answer 1

Marks (x)	Frequency (f)	Cumulative Frequency
0	150	150
10	142	292
20	130	422
30	120	542
40	72	614
50	30	644
60	12	656
70	4	660
	N = 660

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

= Size of `((660 + 1)/4)^"th"` value

= Size of (165.25)^th value

Q₁ = 10

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

= Size of 3(165.25)^th value

= Size of (495.75)^th value

Q₃ = 30

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

= `1/2 (30 - 10)`

= `20/2`

= 10

Co-efficient of Quartile deviation = `("Q"_3 - "Q"_1)/("Q"_3 + "Q"_1)`

= `(30 - 10)/(30 + 10)`

= `20/40`

= `1/2`

= 0.5