# The combined mean of three groups is 12 and the combined mean of first two groups is 3.If the first ,second and third groups have 2,3 and 5 items respectively, then mean if third group is?

Dear Student,

Given : The combined mean of three groups is 12 .

Let sum of observation of first group =  x1 , sum of observation of second group =  x2  and sum of observation of third group =  x3 ,

Also given : the first ,second and third groups have 2 , 3 and 5 items respectively , So

,

x1 + x2  + x3 =  120                                                   ---- ( 1 )

And

The combined mean of first two groups is 3.So

,

x1 + x2 =  15                                                          ---- ( 2 )

Now we subtract equation 2 from equation 1 we get

x3 =  105

Therefore,

Mean if third group = $\frac{105}{5}$ = 21                                                      ( Ans )