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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.