Q. 154.7( 13 Votes )

# If the median of

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.

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