Question

Solve the following :

Calculate D₇ for the following data.

Profit (in crores ₹)	10-20	20-30	30-40	40-50	50-60	60-70
No. of firms	20	30	70	48	32	50

Answer 1

Profit (in crores ₹)	No. of firms	cf
10-20	20	20
20-30	30	50
30-40	70	120
40-50	48	168
50-60	32	200
60-70	50	250
	N = 250

D₇ = Size of 7`(n/10)^"th observation"`

= Size of 7`(250/10)^"th observation"`

= Size of 7`(25)^"th observation"`

= Size of 175^{th observation}

Hence, decile class = 50-60

L = 50, F = 32, cf = 168, N = 250, H = 10

D₇ = 1+`(((7n)/10-cf))/fxxh`

D₇ = 50+`(((7(250))/10-168))/32xx10`

D₇ = 50+`(((1750)/10-168))/32xx10`

D₇ = 50+`((175-168))/32xx10`

D₇ = 50+`(7)/32xx10`

D₇ = 50+`(70)/32`

D₇ = 50 + 2.1875

D₇ = 52.1875.