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# If the median of a distribution given below is 28.5 then, find the value of an x &y. Class Interval Frequency 0-10 5 10-20 x 20-30 20 30-40 15 40-50 y 50-60 5 Total 60

Given that median is 28.5 and $$n \ = \ \sum f_i \ = \ 60$$

Here n = 60
$$\Rightarrow \ \frac{n}{2} \ = \ 30$$

Since the median is given to be 28.5, thus the median class is 20-30.

$$\therefore$$ l = 20, h = 10, f = 20 and cf = 5 + x

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

$$\Rightarrow \ 28.5 \ = \ 20 \ + \ \frac{30 \ - \ 5 \ - \ x}{20} \ × \ 10$$

$$\Rightarrow \ 57 \ = \ 40 \ + \ 25 \ - \ x$$

$$\Rightarrow \ x \ = \ 65 \ - \ 57 \$$

$$\Rightarrow \ x \ = \ 8$$

Also, 45 + x + y = 60
[ As n = 60 ]

$$\Rightarrow \ 45 \ + \ 8 \ + \ y \ = \ 60$$

$$\Rightarrow \ y \ = \ 60 \ - \ 53 \$$

$$\Rightarrow \ y \ = \ 7$$

$$\therefore$$ x = 8, y = 7