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### 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${\left(\frac{n}{100}\right)}^{\text{th observation}}$

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

= Size of 15(1)th observation

= Size of 15th observation

= Size of 15th observation lies in cf 15

Hence, percentile class = 10-20

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

P15 = l +$\frac{\left(\frac{15n}{100}-cf\right)}{f}×h$

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

P15 = 10 +$\frac{\left(\frac{1500}{100}-5\right)}{10}×10$

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

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

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

P15 = 10 + 10

P15 = 20