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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.

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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

 


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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