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Question

If the median of the distribution given below is $$28.5$$, find the values of $$x$$ and $$y$$.
Class-interval$$0 - 10$$$$10 - 20$$$$20 - 30$$$$30 - 40$$$$40 - 50$$$$50 - 60$$Total
Frequency$$5$$$$x$$$$20$$$$15$$$$y$$$$5$$$$60$$


Solution

Here, it is given that Median $$= 28.5$$ and $$n = \sum f_i = 60$$
Cummulative frequency table for the following data is given.

Here $$n=60\Rightarrow \dfrac n2 = 30$$
Since, median is $$28.5$$, median class is $$20-30$$
Hence, $$l = 20, h = 10, f=20, c.f. = 5+x$$
Therefore, Median $$= l+\bigg(\cfrac{\dfrac n2 - cf}{f}\bigg)h$$
$$28.5= 20 + \bigg(\cfrac{30-5-x}{20}\bigg)10$$
$$\Rightarrow 28.5=20 + \cfrac{25-x}{2}$$
$$\Rightarrow 8.5\times 2 = 25-x$$
$$\Rightarrow x = 8$$

Also, $$45+x+y = 60$$
$$\Rightarrow y = 60-45-x = 15-8 = 7$$.

Hence, $$x=8, y=7$$

628931_604243_ans.png

Mathematics

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