If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of

f
1

and
f
2

are ____ and ____, respectively.Class IntervalFrequency0-10f110-20520-30930-401240-50f250-60360-702

Question

If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of

f
    1
   
    and 
    f
    2

are ____ and ____, respectively.Class IntervalFrequency0-10f110-20520-30930-401240-50f250-60360-702

Accepted Answer

If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of f1and f2 are 3 and 6, respectively.Class IntervalFrequency0-10f110-20520-30930-401240-50f250-60360-702Given that the median of the following frequency distribution is 32.5 and the sum of frequencies is 40.Class IntervalFrequency0-10f110-20520-30930-401240-50f250-60360-702The cumulative frequency distribution will be:Class IntervalFrequencyCumulative frequency0-10f1f110-205f1+520-309f1+5+9= f1+1430-4012f1+14+12= f1+2640-50f2f1+26+ f2=f1 + f2+2650-603f1+ f2+26+3= f1+ f2+2960-702f1+ f2+29+2= f1+ f2+31The formula for median:

M=l+
    
     h×

N
          2
         
         −cf
        f

where,

l=
   the lower limit of the median class,

N=
    ∑ 
     frequency
   
   , and

cf=
   cumulative frequency.

f
        1
       
       +
        f
        2
       
       +31=40

f
        1
       
       +
        f
        2
       
       =9

f
        2
       
       =9−
        f
        1

The median is 32.5 which lies in class interval

30−40
   .Hence, the median class

=30−40
  .So,

l=30,

N
      2
     
     =
      
       40
      2
     
     =20,

f=12,

and

cf=14+
    f
    1

Substituting values in formula of median, we get:

30+

20−
            
             14+
              f
              1

12

×10=32.5

6−
          f
          1

12
       
       ×10=2.5

6−
        f
        1
       
       =3

f
        1
       
       =3

Substitute the value of

f
    1

in

f
    2
   
   =9−
    f
    1

,

⇒
        f
        2
       
       =9−3

⇒
        f
        2
       
       =6

Hence, the values of

f
    1

and

f
    2

are

3
   and

6
   respectively.

If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of $f 1 and f 2$ are and , respectively.

Class Interval
Frequency
0-10
$f_{1}$
10-20
5
20-30
9
30-40
12
40-50
$f_{2}$
50-60
3
60-70
2

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Class Interval	Frequency
0-10	$f_{1}$
10-20	5
20-30	9
30-40	12
40-50	$f_{2}$
50-60	3
60-70	2

Class Interval	Frequency	Cumulative frequency
0-10	$f_{1}$	$f_{1}$
10-20	5	$f_{1}$ +5
20-30	9	$f_{1}$ +5+9= $f_{1}$ +14
30-40	12	$f_{1}$ +14+12= $f_{1}$ +26
40-50	f2	$f_{1}$ +26+ $f_{2}$ = $f_{1}$ + $f_{2}$ +26
50-60	3	$f_{1}$ + $f_{2}$ +26+3= $f_{1}$ + $f_{2}$ +29
60-70	2	$f_{1}$ + $f_{2}$ +29+2= $f_{1}$ + $f_{2}$ +31

If the median of the following frequency distribution is 32.5 and the sum of frequencies is 40, then the values of f 1 and f 2 are ____ and ____, respectively.Class IntervalFrequency0-10f110-20520-30930-401240-50f250-60360-702