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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 c)

11-13

13-15

15-17

17-19

19-21

21-23

23-35

Number of children

7

6

9

13

f

5

4


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Solution

To determine the missing frequency, we will use the mean formula.

Here, mean = x = 18

Class interval

Number of children (fi)

Class-mark (xi)

fixi

11-13

7

12

84

13-15

6

14

84

15-17

9

16

144

17-19

13

18 = A

234

19-21

f

20

20f

21-23

5

22

110

23-35

4

24

96

Total

fi = 44 + f

fixi = 752 + 20f

Formula

The mean formula is

Mean = x̄ = fixifi

18 = (752+20f)(44+f) 18(44 + f) = (752 + 20f) 792 + 18f = 752 + 20f 792 + 18f = 752 + 20f 792 752 = 20f 18f 40 = 2f f = 20

Hence, the missing frequency, f = 20.


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