Question

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

Daily pocket allowance (in Rs)	11­ − 13	13­ − 15	15 −17	17 − 19	19 − 21	21 − 23	23 − 25
Number of workers	7	6	9	13	f	5	4

Answer 1

To find the class mark (x_i) for each interval, the following relation is used.

Given that, mean pocket allowance,

Taking 18 as assured mean (a), d_i and f_id_i are calculated as follows.

Daily pocket allowance (in Rs)	Number of children fi	Class mark xi	di = xi − 18	fidi
11­ −13	7	12	− 6	− 42
13 − 15	6	14	− 4	− 24
15 − 17	9	16	− 2	− 18
17 −19	13	18	0	0
19 − 21	f	20	2	2 f
21 − 23	5	22	4	20
23 − 25	4	24	6	24
Total				2f − 40

From the table, we obtain

Hence, the missing frequency, f, is 20.