In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000.

Runs scored
Frequency
2500-3500
5
3500-4500
X
4500-5500
Y
5500-6500
12
6500-7500
6
7500-8500
2

The missing frequencies x and y are and , respectively.

Question

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000.

Runs scored	Frequency
2500-3500	5
3500-4500	X
4500-5500	Y
5500-6500	12
6500-7500	6
7500-8500	2

The missing frequencies x and y are ____ and ____, respectively.

Accepted Answer

The missing frequencies x and y are 15 and 20, respectively.Given:Runs scoredFrequency2500-350053500-4500X4500-5500Y5500-6500126500-750067500-85002We know that the formula of median is

Median =l+
    
     h×

N
          2
         
         −cf
       
      f

where,

l
  =lower limit of the median class,

h
  =size of the median class,

f
  = frequency of the median class,

N
  = sum of frequencies and

cf
   =cumulative frequency of the class just preceding the median class.The cumulative frequency distribution table will be:Runs scoredFrequencyCumulative frequency2500-3500553500-4500x5+x4500-5500y5+x+y5500-6500125+x+y+12=17+x+y6500-7500617+x+y+6=23+x+y7500-8500223+x+y+2=25+x+y=N N=Σfi=60 (given)

25+x+y=60

x+y=35......
        1

Calculating median:

Median =l+
    
     h×

N
          2
         
         −cf
       
      f

5000=4500+
    
     1000×

60
        2
       
       −
        
         5+x
       
      y

500=1000×

30−5−x
      y

y=50−2x.......
    2
   
  Solve equations 1 and 2, we get

x=15,y=20
  .Thus, the missing frequencies x and y are 15,20.

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000.

Runs scored
Frequency
2500-3500
5
3500-4500
X
4500-5500
Y
5500-6500
12
6500-7500
6
7500-8500
2

The missing frequencies x and y are and , respectively.

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Runs scored	Frequency	Cumulative frequency
2500-3500	5	5
3500-4500	x	5+x
4500-5500	y	5+x+y
5500-6500	12	5+x+y+12=17+x+y
6500-7500	6	17+x+y+6=23+x+y
7500-8500	2	23+x+y+2=25+x+y=N
	N=Σfi=60 (given)

In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000.Runs scoredFrequency2500-350053500-4500X4500-5500Y5500-6500126500-750067500-85002The missing frequencies x and y are ____ and ____, respectively.

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Detailed Solution

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In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000.

Runs scored
Frequency
2500-3500
5
3500-4500
X
4500-5500
Y
5500-6500
12
6500-7500
6
7500-8500
2

The missing frequencies x and y are and , respectively.