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# If the median of the distribution given below is 28.5, find the values of x and y.

2. If the median of the distribution given below is 28.5, find the values of x and y.

Answers (1)
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 Class Number of consumers $f_i$ Cumulative Frequency 0-10 5 5 10-20 x 5+x 20-30 20 25+x 30-40 15 40+x 40-50 y 40+x+y 50-60 5 45+x+y $\sum f_i = N$ = 60

$\dpi{100} N= 60 \implies \frac{N}{2} = 30$

Now,
Given median = 28.5 which lies in the class 20-30

Therefore, Median class = 20-30
Frequency corresponding to median class, f = 20
Cumulative frequency of the class preceding the median class, c.f. = 5 + x
Lower limit, l = 20; Class height, h = 10

$Median = l + \left (\frac{\frac{n}{2}-c.f}{f} \right ).W$
$\\ \implies28.5= 20 + \left (\frac{30-5-x}{20} \right ).10 \\ \\ \implies8.5=\frac{25-x}{2} \\ \implies 25-x = 8.5(2) \\ \implies x = 25 - 17 = 8$

Also,

$\\ 60 = 45 + x+y \\ \implies x+y = 60-45 = 15 \\ \implies y = 15-x = 15-8 \ \ \ (\because x =8) \\ \implies y = 7$

Therefore, required values are: x=8 and y=7

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