Question

If the mean of the following observations is 54, find the value of p.

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	7	p	10	9	13

Answer 1

Class	Frequency (f)	Mid value (x)	fx
0 – 20	7	10	70
20 – 40	p	30	30p
40 – 60	10	50	500
60 – 80	9	70	630
80 – 100	13	90	1170
Total	39 + p		2370 + 30p

`barx = (sumfx)/(sumf) = (2370 + 30p)/(39 + p)`  ...(i)

Here mean = 54  ...(ii) 

From (i) and (ii)

`(2370 + 30p)/(39 + p) = 54` 

`=>` 2370 + 30p = 2106 + 54p 

`=>` 54p – 30p = 2370 – 2106

`=> p = 264/24 = 11`