Q. The distribution below gives the weights of 30 students of a class.
Find the median weight of the students.
Weight (in kg) | 40 - 45 | 45 - 50 | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 |
Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
Sol:
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class
40 - 45
45 - 50
60 - 65
65 - 70
2
3
6
3
2
25
28
c.f
Here
n
2
=
30
2
= 15
which lies in the class 55 - 60
∴ Median class is 55 - 60
l = 55
Median =
l +
n
2
– c.f.
f
x h
= 55 +
15 – 13
6
x 5
Weight (in kg)
Number of students
frequency
19
, h = 5,
f = 6,
c.f. = 13
55 - 60
6
f
13
50 - 55
8
2 + 3 = 5
5 + 8 = 13
= 55 +
10
6
1.67
Which c.f is greater than
Or equal to ?
n
2
Cumulative frequency of the class preceeding the median class (c.f)
5
70 - 75
2
30
= 55 + 1.67
∴ Median = 56.67 kg
Exercise 14.3 – Q.7