Solve the following : Find out P50 for the following data. Wages (in ₹) (x) Number of workers 0-20 4 20-40 6 40-60 10 60-80 25 80-100 15 - Economics

QUESTION

Solve the following :

Find out P₅₀ for the following data.

Wages (in ₹) (x)	Number of workers
0-20	4
20-40	6
40-60	10
60-80	25
80-100	15

SOLUTION

Wages (in ₹) (x)	Number of workers	cf
0-20	4	4
20-40	6	10
40-60	10	20
60-80	25	45
80-100	15	60
	N=60

P₅₀ = size of 50${\displaystyle {\left(\frac{n}{100}\right)}^{\text{th observation}}}$

= size of 50${\displaystyle {\left(\frac{60}{100}\right)}^{\text{th observation}}}$

= size of 50${\displaystyle {\left(0.6\right)}^{\text{th observation}}}$

size of ${\displaystyle {30}^{\text{th observation}}}$

Size of ${\displaystyle {30}^{\text{th observation}}}$ lies in cf 45

Hence , percentile class = 60-80

L= 60 , f= 25, cf= 20 ,n= 60, h= 20

P₅₀ = 1+${\displaystyle \frac{(\frac{50n}{100}-cf)}{f}\times h}$

P₅₀ = 60+${\displaystyle \frac{\frac{50\left(60\right)}{100}-20}{25}\times 20}$

P₅₀ = 60+${\displaystyle \frac{(\frac{3000}{100}-20)}{25}\times 20}$

P₅₀ = 60+${\displaystyle \frac{(30-20)}{25}\times 20}$

P₅₀ = 60+${\displaystyle \frac{\left(10\right)}{25}\times 20}$

P₅₀ = 60+${\displaystyle \frac{\left(200\right)}{25}\times 20}$

P₅₀ = 60+8

P₅₀ = 68