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

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

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

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

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

Hence , percentile class = 60-80

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

P50 = 1+$\frac{\left(\frac{50n}{100}-cf\right)}{f}×h$

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

P50 = 60+$\frac{\left(\frac{3000}{100}-20\right)}{25}×20$

P50 = 60+$\frac{\left(30-20\right)}{25}×20$

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

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

P50 = 60+8

P50 = 68