Question

If the mean of the following frequency distribution is 18, find the missing frequency.

Class interval	11 – 13	13 – 15	15 – 17	17 – 19	19 – 21	21 – 23	23 – 25
Frequency	3	6	9	13	f	5	4

Answer 1

Class	Mid point `(bb(x_i))`	Frequency `(bb(f_i))`	`bb(f_ix_i)`
11 – 13	12	3	36
13 – 15	14	6	84
15 – 17	16	9	144
17 – 19	18	13	234
19 – 21	20	f	20f
21 – 23	22	5	110
23 – 25	24	4	96
		`sumf_i = 40 + f`	`sumf_ix_i = 704 + 20f`

Mean = `(sumf_ix_i)/(sumf_i)`

∴ 18 = `(704 + 20f)/(40 + f)`  ...[∵ Given, mean = 18]

⇒ 18(40 + f) = 704 + 20f

⇒ 720 + 18f = 704 + 20f

⇒ 2f = 16

⇒ f = 8

So, missing frequency f is 8.