The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

It is given that the median of the following data is

525

and the total frequency is

100

From the given table, we have the frequency distribution table as,

We have,

N = \sum f_{i} = 100

\Rightarrow 76 + x + y = 100

\Rightarrow x + y = 24

It is given that the median is

525

. Clearly, it lies in the class

500 - 600 .

The general formula for median is given as,
Median

= l + \frac{\frac{N}{2} - C . F .}{f} \times h

Where,
l = lower limit of median class

= 500 .

C.F. = C.F. of previous class

= (36 + x) .

f = frequency of median class

= 20 .

h = width of median class = upper limit - lower limit

h = 600 - 500

h = 100

Substituting all the above values in given formula of median, we obtain,

\Rightarrow 525 = 500 + \frac{50 - (36 + x)}{20} \times 100

\Rightarrow 525 - 500 = (14 - x) \times 5

\Rightarrow 25 = 70 - 5 x

\Rightarrow 5 x = 45

\Rightarrow x = 9

Putting

x = 9

x + y = 24

, we get

y = 15 .

Therefore,

x = 9

and

y = 15 .

Hence, option (4) is correct.

The median of the following data is $525$ .

Find the values of $x$ and $y$ , if the total frequency is $100$ .