Question 30
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is 18. Find the missing frequency k.
Daily Pocket allowance (in rupees)
11 − 13
13 − 15
15 - 17
17 − 19
19 − 21
21 − 23
23 − 25
Number of Students
3
6
9
13
k
5
4
Daily pocket allowance (in Rs) Number of workers 11 – 13 3 13 – 15 6 15 – 17 9 17 – 19 13 19 – 21 k 21 – 23 5 23 – 25 4 Class mark
(xi)
12
14
16
18
20
22
24
Fixi
36
84
144
234
20k
110
96
704+20k
18(40 + k) = 704 + 20k
18(40)+ 18(k) = 704 + 20k
720 + 18k = 704 + 20k
720 – 704 = 20k – 18k
16 = 2k
k = 16/2
k = 8
Distance
0 − 10
10 − 20
20 − 30
30 − 40
40 − 50
50 − 60
60 − 70
Number of Students
4
5
13
20
14
8
4
Distance (in m)
Number of workers( fi )
Cumulative frequency
0 – 10
4
4
10 – 20
5
4 + 5 = 9
20 – 30
13
9 + 13 = 22
30 – 40
20
22 + 20 = 42
40 – 50
14
42 + 14 = 56
50 – 60
8
56 + 8 = 64
60 – 70
4
64 = 4 = 68
∑▒𝑓𝑖 = 68
Distance (in m)
Number of workers( fi )
Less than 10
4
Less than 20
9
Less than 30
22
Less than 40
42
Less than 50
56
Less than 60
64
Less than 70
68
∑▒𝑓𝑖 = 68
So, N = 68
∴ 𝑁/2 = 68/2 = 34
We draw a line parallel to x-axis where
Number of students = 34
Where the line intersects the curve at x-axis, it is the median
∴ Median distance = 36 m

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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