The mean of the following distribution is 18. Find the . . .

Question : The mean of the following distribution is 18. Find the frequency of the class 19-21.

Class Intervals	Frequency
11-13	3
13-15	6
15-17	9
17-19	13
19-21	f
21-23	5
23-25	8
Total	Σfi=40+f

Doubt by Gauri

Solution : 
 

Class Intervals (CI)	Frequency (Fi)	Class Marks (xi)	di=xi-a	fidi
11-13	3	12	-6	-18
13-15	6	14	-4	-24
15-17	9	16	-2	-18
17-19	13	18 = a	0	0
19-21	f	20	2	2f
21-23	5	22	4	20
23-25	4	24	6	24
Total	Σfi=40+f			Σfidi=-16+2f

Mean (x̄) = 18

By Assumed Mean Method

a = 18

Σfidi=-16+2f

Σfi=40+f

x̄ = a + Σfidi/Σfi
18 = 18 + (-16+2f)/(40+f)

18-18 = (-16+2f)/(40+f)
0 = (-16+2f)/(40+f)
0×(40+f) = -16+2f
0 = -16+2f
16=2f
16/2 = f

f = 8