# 19.Find the missing frequencies f1  , f2 and f3 in the following frequency distribution , when it is given taht f2 : 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,

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 $\sum _{}$f = x + 7 y + 36 $\sum _{}$fx = 30 x + 410 y + 1880

Also given :  Sum of frequency $\sum _{}$f = 120 , So

x + 7 y + 36 =  120 ,

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

And mean of given data  =  50

So,
Mean  = $\frac{{\sum }_{}^{}fx}{\sum _{}f}$ = 50 , Substitute values we get :

$⇒$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 )