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If the median of the distribution is $28.5$ , what are the values of x and y?

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8, 7

9, 7

6, 8

7, 9

answer is A.

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Detailed Solution

It is given the median of the distribution is

28.5

We create a cumulative frequency table for the given data.

Class Interval	Frequency(f)	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
	N = 60

From the table, we get

ΣF = 60

\Rightarrow x + y + 45 = 60

\Rightarrow x + y = 15

……[1]
Given median of the data =

28.5

We know that,
Median =

L + \frac{\frac{N}{2} - C}{f} \times w

Here

L

is lower limit of class

20 - 30

f

is frequency of class

20 - 30,

w

is width of class

C

is cumulative frequency of previous class

N

ΣF

From the data, we get

L = 20

\frac{N}{2} = \frac{60}{2}

\Rightarrow \frac{N}{2}

30

C = x + 5

w = 30 - 20 = 10

f = 20

Putting the values in the formula, we get

\Rightarrow M = 20 + \frac{30 - (x + 5)}{20} \times 10

\Rightarrow 28.5 = 20 + \frac{25 - x}{20} \times 10

\Rightarrow 8.5 = \frac{25 - x}{2}

\Rightarrow x = 8

From [1], we get

x + y = 15

\Rightarrow 8 + y = 15

\Rightarrow y = 7

Thus, the value of

x is 8 and  y is 7 .

Hence, the correct option is 1.

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