19.Find the missing frequencies f , f2 and f3 in the following frequency distribution , when it is given taht f: f3 = 4 : 3 , and mean = 50 

 
Class interval Frequency
0-20
20-40
40-60
60-80
80-100

17
f1
f2
f3
19


 
Total 120

Dear Student,

Please find below the solution to the asked query:

Here we assume f1 = x  ,

Given f2f3 = 4 : 3 , We assume ratio coefficient =  y , So 

f2 = 4 y and f3 = 3 y 

We form table from given information , As  :
Class Mid point ( x ) Frequency ( f ) fx
0 - 20  10 17  170
20 - 40  30  x  30 x
40 - 60  50  4 y  200 y
60 - 80  70  3 y  210 y
80 - 100  70 19  1710
       
    f = x + 7 y + 36 fx = 30 x + 410 y + 1880
       

Also given :  Sum of frequency f = 120 , So

x + 7 y + 36 =  120 ,

x + 7 y = 84                                                                    --- ( 1 )

And mean of given data  =  50 


So,
Mean  = fxf = 50 , Substitute values we get :

30 x + 410 y + 1880120 = 50
30 x  + 410 y  + 1880 =  6000

30 x  + 410 y  =  4120

3 x  + 41 y  =  412                                                     --- ( 2 )

Now we multiply by 3 in equation 1 and get :


3 x + 21 y = 252                                                             --- ( 3 )


Now we subtract equation 3 from equation 2 and get :

20 y  =  160 ,

y  = 8 , Substitute that value in equation 1 we get :

x  + 7 ( 8 ) =  84 ,

x  + 56 =  84 ,

x = 28

Therefore,

f1 = 28 and f2 = 4 ( 8 ) =  32 and   f3 = 3 ( 8 ) =  24                                                    ( Ans )

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