Question

If the median of 1000 observations, given below is 525. Find the values of 'x' and 'y'.
Class Interval
0-100 100-200 200-300 300-400 400-500
Frequency
2.
5
12
17
Х
ity Education Management Pvt. Ltd.​

Answer 1

Answer:

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.