The distribution below gives the weight of 30 students in a class. Find the median weight of students:
Weight (in kg): | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 |
No. of students: | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
Given:
The distribution gives the weight of 30 students in a class.
To do:
We have to find the median weight of students.
Solution:
![](/assets/questions/media/158630-45028-1620743513.jpg)
Here,
$N = 30$
$\frac{N}{2} = \frac{30}{2} = 15$
The cumulative frequency just greater than $\frac{N}{2}$ is 19 and the corresponding class is 55 – 60.
This implies, 55– 60 is the median class.
Therefore,
$l = 55, f = 6, F = 13$ and $h = (60 - 55) = 5$
Medain $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$
$=55+\frac{15-13}{6} \times 5$
$=55+\frac{2}{6} \times 5$
$=55+\frac{5}{3}$
$= 55 + 1.67$
$= 56.67$
The median weight of students is 56.67 kg.
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