Question

Q.21: If the median of the following frequency distribution is 525 in the table given below, find the value
of x and y, if total frequency is 100.
Variable
0-100
100-
200
5
200-
300
Х
300-
400
12
400-
500
17
500-
600
20
600-
700
Y
700-
800
9
800-
900
7.
900-
1000
4
Frequency 2​

Answer 1

Answer:

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Answer 2

Answer:

Correct option is

D

x=9 y=15

Computation of Median

Class interval Frequency (f) Cumulative frequency (cf)

0-100 2 2

100-200 5 7

200-300 x 7+x

300-400 12 19+x

400-500 17 36+x

500-600 20 56+x

600-700 y 56+x+y

700-800 9 65+x+y

800-900 7 72+x + y

900-1000 4 76+x + y

Total = 100

We have,

N=∑f

i

=100

⇒76+x+y=100⇒x+y=24

It is given that the median is 525. Clearly, it lies in the class 500−600

∴l=500,h=100,f=20,F=36+x and N=100

Now,

Median=i+

f

2

N

−F

×h

⇒525=500+

20

50−(36+x)

×100

⇒525−500=(14−x)×5

⇒25=70−5x⇒5x=45⇒x=9

Putting x=9 inx+y=24, we get y=15.

Hence, x=9and y=15.