Question

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

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, $$x=8, y=7$$Mathematics

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