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 - Economics

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

SOLUTION

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

P₃ = Size of 15${\displaystyle {\left(\frac{n}{100}\right)}^{\text{th observation}}}$

= Size of 15${\displaystyle {\left(\frac{100}{100}\right)}^{\text{th observation}}}$

= 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 +${\displaystyle \frac{(\frac{15n}{100}-cf)}{f}\times h}$

P₁₅ = 10+${\displaystyle \frac{(\frac{15\left(100\right)}{100}-5)}{10}\times 10}$

P₁₅ = 10 +${\displaystyle \frac{(\frac{1500}{100}-5)}{10}\times 10}$

P₁₅ = 10 +${\displaystyle \frac{(15-5)}{10}\times 10}$

P₁₅ = 10 +${\displaystyle \frac{\left(10\right)}{10}\times 10}$

P₁₅ = 10 +${\displaystyle \frac{100}{10}}$

P₁₅ = 10 + 10

P₁₅ = 20