Question

If the median of the distribution given below is 27 , find the missing frequencies x and y​

Answer 1

C.I f  c.f  

0 - 10  5  5  

10 - 20   x  5+x  

20 - 30 20 25+x  

30 - 40 14  39+x  

40 - 50 y  39+x+y  

50 - 60  8  47+x+y.  

Total  68.    

here, 47+x+y =68 _____ (1)

Given that, median = 27.

Hence the median class is 20 - 30.

∴l=20,  

2

m

​  

=  

2

68

​  

=34,c.f=5+x,h=10,f=20.

we know, median =l+  

f

2

m

​  

−c.f

​  

×h

27=20+  

20

34−(5+x)

​  

×10

27=20+  

2

34−5−x

​  

 

⇒54=40+34−5−x.

⇒=69−x.

⇒x=69−54

⇒x=15

from (1), y = 68-47-15 = 6

Hence x = 15, y = 6