Question:
The distribution below gives the weight of 30 students in a class. Find the median weight of students:
Solution:
We prepare the cumulative frequency table, as given below.
We have, $N=30$
So, $\frac{N}{2}=15$
Now, the cumulative frequency just greater than 15 is 19 and the corresponding class is $55-60$.
Therefore, $55-60$ is the median class.
Here, $l=55, f=6, F=13$ and $h=5$
We know that
Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$
$=55+\left\{\frac{15-13}{6}\right\} \times 5$
$=55+\frac{2 \times 5}{6}$
$=55+\frac{10}{6}$
$=55+1.667$
$=56.667$
Hence, the median weight of students is 56.67 kg.
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