Question

Solve the following :

Calculate P₁₅ for the following data.

Investment (₹ in lakhs)	0-10	10-20	20-30	30-40	40-50	50-60
No. of firms	5	10	25	30	20	10

Answer 1

Investment (₹ in lakhs)	No. of firms	cf
0-10	5	5
10-20	10	15
20-30	25	40
30-40	30	70
40-50	20	90
50-60	10	100
	N = 100

P₁₅ = Size of 15`(n/100)^"th" "observation"`

= Size of 15`(100/100)^"th" "observation"`

= Size of 15(1)^th observation

= Size of 15^th observation

= Size of 15^th observation lies in cf 15

Hence, percentile class = 10-20

L = 10, f = 10, cf = 5, n = 100, h = 10

P₁₅ = L +`(((15n)/100-cf))/fxxh`

P₁₅ = 10+`(((15(100))/100-5))/10xx10`

P₁₅ = 10 +`((1500/100-5))/10xx10`

P₁₅ = 10 +`((15-5))/10xx10`

P₁₅ = 10 +`((10))/10xx10`

P₁₅ = 10 +`(100)/10`

P₁₅ = 10 + 10

P₁₅ = 20 lakhs