Q. 154.7( 13 Votes )
If the median of
Answer :
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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