If the median of the following data is 32, let us determine the values of x and y when the sum of the frequencies is 100

Given is, median of the data = 32

Sum of frequency, N = 100

To find: x and y

Let us show cumulative frequency in a table.

Here, we have got

N = 75 + x + y

But, N = 100

⇒ 75 + x + y = 100

⇒ x + y = 100 – 75

⇒ x + y = 25 …(i)

For median:

We have, total frequency, N = 100

N/2 = 100/2 = 50

∵ median = 32

It lies in the interval 30 – 40.

Thus, median class = 30 – 40

Median is given by

Where,

L = Lower class limit of median class = 30

N/2 = 50

cf = cumulative frequency of the class preceding median class = 35 + x

f = frequency of the median class = 30

h = class interval of the median class = 10

Substituting these values in the formula of median, we get

⇒

⇒

⇒

⇒

⇒ 96 = 105 – x

⇒ x = 105 – 96

⇒ x = 9

Substituting x = 9 in equation (i),

x + y = 25

⇒ 9 + y = 25

⇒ y = 25 – 9

⇒ y = 16

Thus, x = 9 and y = 16.