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

No. of childrens

7

6

9

13

f

5

4

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Solution

Here, we have

top enclose x space equals space 18 comma space sum from blank to blank of f subscript i equals 44 plus f space a n d space sum from blank to blank of f subscript i x subscript i equals 752 space plus space 20 f

We know,

top enclose straight x space equals space fraction numerator begin display style sum from blank to blank of end style straight f subscript straight i straight x subscript straight i over denominator begin display style stack sum straight f subscript straight i with blank below and blank on top end style end fraction

rightwards double arrow

18 space equals space fraction numerator 752 plus 20 straight f over denominator 44 plus straight f end fraction

rightwards double arrow

18 (44 + f) = 752 + 20f

rightwards double arrow

792 + 18f = 752 + 20f

rightwards double arrow

18f - 20f = 752 - 792

rightwards double arrow

-2f = -40

rightwards double arrow

f = 20
Hence the Missing frequency is 20.

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Daily pocket allowance (in Rs.)	11-13	13-15	15-17	17-19	19-21	21-23	23-25
No. of childrens	7	6	9	13	f	5	4