### 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 - Economics

#### 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

#### SOLUTION

 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${\left(\frac{n}{10}\right)}^{\text{th observation}}$

= Size of 7${\left(\frac{250}{10}\right)}^{\text{th observation}}$

= Size of 7${\left(25\right)}^{\text{th observation}}$

= Size of 175th observation

Hence, decile class = 50-60

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

D7 = 1+$\frac{\left(\frac{7n}{10}-cf\right)}{f}×h$

D7 = 50+$\frac{\left(\frac{7\left(250\right)}{10}-168\right)}{32}×10$

D7 = 50+$\frac{\left(\frac{1750}{10}-168\right)}{32}×10$

D7 = 50+$\frac{\left(175-168\right)}{32}×10$

D7 = 50+$\frac{7}{32}×10$

D7 = 50+$\frac{70}{32}$

D7 = 50 + 2.1875

D7 = 52.1875.