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

Answer 1

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 `("n"/100)^"th"` observation

= size of 50`(60/100)^"th"` observation

= size of 50 (0.60)^th observation

= size of 30^th observation

c.f. which is just greater than (or equal to) 30 is 45.

l = 60, f = 25, C.F. = 20, n = 60, h = 20

`"P"_"i" = l + (("in"/100 - cf)/f) xx h`

P₅₀ = l + `(((50"n")/100 - "c.f.")/"f") xx "h"`

P₅₀ = `60 + (((50 xx 60)/100 - 20)/25) xx 20`

= `60 + ((30 - 20)/25) xx 20`

= `60 + (10/25) xx 20`

= `60 + (200/25)`

= 60 + 8

= 68