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.

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

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.

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

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.