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

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

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

= Size of 175^{th observation}

Hence, decile class = 50-60

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

D₇ = 1+${\displaystyle \frac{(\frac{7n}{10}-cf)}{f}\times h}$

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

D₇ = 50+${\displaystyle \frac{(\frac{1750}{10}-168)}{32}\times 10}$

D₇ = 50+${\displaystyle \frac{(175-168)}{32}\times 10}$

D₇ = 50+${\displaystyle \frac{7}{32}\times 10}$

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

D₇ = 50 + 2.1875

D₇ = 52.1875.