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# 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

 Class Interval Frequency Cumulative frequency 40-45 2 2 45-50 3 5 50-55 8 13 55-60 6 19 60-65 6 25 65-70 3 28 70-75 2 30

We have n = 30 $$\Rightarrow \ \frac{n}{2} \ = \ 15$$

The cumulative frequency just greater than $$\frac{n}{2}$$ is 19 and the corresponding class is 55 - 60.

Thus, 55 - 60 is the median class such that :

$$\frac{n}{2} = 15 , l = 55 , f = 6 , cf = 13 \ and \ h = 5$$

Median $$= \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h$$

$$= \ 55 \ + \ ( \frac{15 \ - \ 13}{6}) \ × \ 5$$

$$= \ 55 \ + \ \frac{2}{6} \ × \ 5 \ =$$

$$55 \ + \ 1.67 \ = \ 56.67$$

$$\therefore$$ The median weight = 56.67 kg .